78 (number): Difference between revisions

← 77 78 79 →
← 70 71 72 73 74 75 76 77 78 79 → List of numbers; Integers; ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seventy-eight
Ordinal	78th; (seventy-eighth)
Factorization	2 × 3 × 13
Divisors	1, 2, 3, 6, 13, 26, 39, 78
Greek numeral	ΟΗ´
Roman numeral	LXXVIII
Binary	10011102
Ternary	22203
Senary	2106
Octal	1168
Duodecimal	6612
Hexadecimal	4E16

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78 (seventy-eight) is the natural number following 77 and preceding 79.

In mathematics

78 as the sum of four distinct nonzero squares

78 is:

the 4th discrete tri-prime; or also termed Sphenic number, and the 4th of the form (2.3.r).^[1]
an abundant number with an aliquot sum of 90; within an aliquot sequence of nine composite numbers (78, 90,144,259,45,33,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
a semiperfect number, as a multiple of a perfect number.
the 12th triangular number.^[2]
a palindromic number in bases 5 (303₅), 7 (141₇), 12 (66₁₂), 25 (33₂₅), and 38 (22₃₈).
a Harshad number in bases 3, 4, 5, 6, 7, 13 and 14.
an Erdős–Woods number, since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member.^[3]
the dimension of the exceptional Lie group E₆ and several related objects.
the smallest number that can be expressed as the sum of four distinct nonzero squares in more than one way: $8^{2}+3^{2}+2^{2}+1^{2}$ , $7^{2}+4^{2}+3^{2}+2^{2}$ or $6^{2}+5^{2}+4^{2}+1^{2}$ (see image).^[4]^[5]

77 and 78 form a Ruth–Aaron pair.

In science

The atomic number of platinum.
The percentage of nitrogen in Earth's atmosphere.

In other fields

78 is also:

In reference to gramophone records, 78 refers those meant to be spun at 78 revolutions per minute. Compare: LP, 33+1⁄3 and 45 rpm. 33 + 45 = 78
A typical tarot deck containing the 21 trump cards, the Fool and the 56 suit cards make up 78 cards
The Rule of 78s is a method of yearly interest calculation
The number used by Martin Truex Jr. and Furniture Row Racing to win the 2017 Monster Energy NASCAR Cup Series championship and 2016 Coca-Cola 600. The team and driver Regan Smith also won the 2011 Showtime Southern 500 with 78. The number is now used by owner-driver B.J. McLeod for Live Fast Motorsports.

References

^ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
^ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
^ Sloane, N. J. A. (ed.). "Sequence A025386 (Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A025378 (Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[1] "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.

[2] "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.

[3] "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.

[4] Sloane, N. J. A. (ed.). "Sequence A025386 (Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[5] Sloane, N. J. A. (ed.). "Sequence A025378 (Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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@@ Line 4: / Line 4: @@
 | divisor = 1, 2, 3, 6, 13, 26, 39, 78
 }}
-'''78''' ('''seventy-eight''') is the [[natural number]] following [[77 (number)|77]] and followed by [[79 (number)|79]].
+'''78''' ('''seventy-eight''') is the [[natural number]] following [[77 (number)|77]] and preceding [[79 (number)|79]].
 ==In mathematics==
+[[File:square-sum-78.png|thumb|78 as the sum of four distinct nonzero squares]]
 '''78''' is:
+*the 4th discrete tri-prime; or also termed [[Sphenic number]], and the 4th of the form (2.3.r).<ref>{{Cite web|url=https://oeis.org/A007304|title=Sloane's A007304 : Sphenic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>
-*the dimension of the [[Simple Lie group#Exceptional cases|exceptional]] Lie group [[E6 (mathematics)|E<sub>6</sub>]] and several related objects.
+*an [[abundant number]] with an [[aliquot sum]] of [[90 (number)|90]]; within an [[aliquot sequence]] of nine composite numbers (78,  [[90 (number)|90]],[[144 (number)|144]],[[259 (number)|259]],[[45 (number)|45]],[[33 (number)|33]],[[15 (number)|15]],[[9 (number)|9]],[[4 (number)|4]],[[3 (number)|3]],[[1 (number)|1]],0) to the Prime in the [[3 (number)|3]]-aliquot tree.
-*a [[sphenic number]], having 3 distinct prime [[factorization|factors]].<ref>{{Cite web|url=https://oeis.org/A007304|title=Sloane's A007304 : Sphenic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>
-*an [[abundant number]] with an aliquot sum of 90.
 *a [[semiperfect number]], as a multiple of a perfect number.
-*the 12th [[triangular number]].
+*the 12th [[triangular number]].<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref>
 *a [[palindromic number]] in bases 5 (303<sub>5</sub>), 7 (141<sub>7</sub>), 12 (66<sub>12</sub>), 25 (33<sub>25</sub>), and 38 (22<sub>38</sub>).
 *a [[Harshad number]] in bases 3, 4, 5, 6, 7, 13 and 14.
 *an [[Erdős–Woods number]], since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member.<ref>{{Cite web|url=https://oeis.org/A059756|title=Sloane's A059756 : Erdős-Woods numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>
+*the dimension of the [[Simple Lie group#Exceptional cases|exceptional]] Lie group [[E6 (mathematics)|E<sub>6</sub>]] and several related objects.
+*the smallest number that can be expressed as the sum of four distinct nonzero [[square number|squares]] in more than one way: <math>8^2+3^2+2^2+1^2</math>, <math>7^2+4^2+3^2+2^2</math> or <math>6^2+5^2+4^2+1^2</math> (see image).<ref>{{cite OEIS|A025386|Numbers that are the sum of 4 distinct nonzero squares in 2 or more ways.}}</ref><ref>{{cite OEIS|A025378|Numbers that are the sum of 4 distinct nonzero squares in exactly 3 ways.}}</ref>
 and 78 form a [[Ruth–Aaron pair]].
@@ Line 22: / Line 24: @@
 ==In science==
 *The [[atomic number]] of [[platinum]].
+*The percentage of [[nitrogen]] in Earth's [[atmosphere]].
 ==In other fields==
@@ Line 27: / Line 30: @@
 is also:
 *In reference to [[gramophone record]]s, '''78''' refers those meant to be spun at 78 [[revolutions per minute]]. Compare: [[gramophone record|LP]], {{frac|[[Thirty three|33]]|1|3}} and [[Forty five|45]] rpm. 33 + 45 = 78
-*A typical [[tarot]] deck containing the 21 [[trump cards]], the [[The Fool (Tarot card)|Fool]] and the 56 suit cards make up 78 cards
+*A typical [[tarot]] deck containing the 21 [[Trump (card games)|trump cards]], the [[The Fool (Tarot card)|Fool]] and the 56 suit cards make up 78 cards
 *The [[Rule of 78s]] is a method of yearly interest calculation
 * The number used by [[Martin Truex Jr.]] and [[Furniture Row Racing]] to win the [[2017 Monster Energy NASCAR Cup Series]] championship and [[2016 Coca-Cola 600]]. The team and driver [[Regan Smith (racing driver)|Regan Smith]] also won the [[2011 Showtime Southern 500]] with 78. The number is now used by owner-driver [[B.J. McLeod]] for [[Live Fast Motorsports]].