363 (number): Difference between revisions

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Cardinal	three hundred sixty-three
Ordinal	363rd; (three hundred sixty-third)
Factorization	3 × 112
Divisors	1, 3, 11, 33, 121, 363
Greek numeral	ΤΞΓ´
Roman numeral	CCCLXIII, ccclxiii
Binary	1011010112
Ternary	1111103
Senary	14036
Octal	5538
Duodecimal	26312
Hexadecimal	16B16

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363 (three hundred [and] sixty-three) is the natural number following 362 and preceding 364.

In mathematics

It is an odd, composite, positive, real integer, composed of a prime (3) and a prime squared (11²).
363 is a deficient number and a perfect totient number.
363 is a palindromic number in bases 3, 10, 11 and 32.
363 is a repdigit (BB) in base 32.
The Mertens function returns 0.^[1]
Any subset of its digits is divisible by three.
363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).
363 can be expressed as the sum of three squares in four different ways: 11² + 11² + 11², 5² + 7² + 17², 1² + 1² + 19², and 13² + 13² + 5².
363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter [1].

References

^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.

This article about a number is a stub. You can help Wikipedia by expanding it.

[1] "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.

[1]

@@ Line 1: / Line 1: @@
-{{Refimprove|date=June 2016}}
+{{One source|date=January 2025}}
 {{Infobox number
 | number = 363
 | divisor = [[1 (number)|1]], [[3 (number)|3]], [[11 (number)|11]], [[33 (number)|33]], [[121 (number)|121]], 363
 }}
-'''363''', three hundred [and] sixty three, is the [[integer]] after 362 and before 364.
+'''363''' ('''three hundred [and] sixty-three''') is the [[natural number]] following [[362 (number)|362]] and preceding [[364 (number)|364]].
 ==In mathematics==
-* 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
 * It is an odd, [[composite number|composite]], [[Positive number|positive]], [[real number|real]] integer, composed of a [[prime number|prime]] (3) and a prime squared (11<sup>2</sup>).
+* 363 is a [[deficient number]] and a [[perfect totient number]].
-* The 363rd day in a year is 29 December (28 December in [[leap year]]s).
 * 363 is a [[palindromic number]] in bases 3, 10, 11 and 32.
-* Any subset of its digits is divisible by three.
 * 363 is a [[repdigit]] (BB) in base 32.
+* The [[Mertens function]] returns 0.<ref>{{cite web|title=Sloane's A028442 : Numbers n such that Mertens' function is zero|url=https://oeis.org/A028442|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-02}}</ref>
-* 363 is a 122-gonal number.
+* Any subset of its digits is divisible by three.
-* 363 is a [[deficient number]].
-* 363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243) [[deficient number]].
+* 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
+* 363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).
-* The [[Mertens function]] returns 0.<ref>{{cite web|title=Sloane's A028442 : Numbers n such that Mertens' function is zero|url=https://oeis.org/A028442|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|accessdate=2016-06-02}}</ref>
-* 363 cubits is the solution given to [[Rhind Mathematical Papyrus]] question 50 – find the side length of an octagon with the same area as a circle 9 [[Ancient Egyptian units of measurement|khet]] in diameter [http://www.seshat.ch/home/rhind6.htm].
 * 363 can be expressed as the sum of three squares in four different ways: 11<sup>2</sup> + 11<sup>2</sup> + 11<sup>2</sup>, 5<sup>2</sup> + 7<sup>2</sup> + 17<sup>2</sup>, 1<sup>2</sup> + 1<sup>2</sup> + 19<sup>2</sup>, and 13<sup>2</sup> + 13<sup>2</sup> + 5<sup>2</sup>.
+* 363 cubits is the solution given to [[Rhind Mathematical Papyrus]] question 50 – find the side length of an octagon with the same area as a circle 9 [[Ancient Egyptian units of measurement|khet]] in diameter [http://www.seshat.ch/home/rhind6.htm].
-*363 is the number of Austin Coon
-==In other fields==
-* The years AD 363 (in base 35 written AD AD) and [[363 BC]] (in base 32 written BB BC).
-* 363 may be associated with the [[messiah]]
-* [[Food additive]] E363 is [[succinic acid]] a [[food acid]].
-* [[363 Padua]] is a (probably typical Main Band) [[asteroid]].
-* 363 is attested in [[Egyptian mythology]]. In the [[Edfu]] texts for example it appears to be associated with [[Thoth]].
-* 363 main keys in numerology : The [[Creativity|Creative]], [[Innovation|Innovative]].
-* [[USS Balch (DD-363)]] was a [[Porter-class destroyer]] in the [[United States Navy]].
-* 363 is the number of communes of the [[Maine-et-Loire]] département in [[France]].
-* 363 is the London ''Laburnum'' dialling code for [[Winchmore Hill]].
-* In [[Unicode]] the [[Macron (diacritic)|macron]] ū is <nowiki>&amp;#363;</nowiki>
-* In May 1877, 363 [[France|French]] deputies passed the vote of no confidence in the [[duc de Broglie]] - the [[Seize Mai]].
-* [[DARPA|Arpa]] [[mailing list]]s are dealt with in {{IETF RFC|363}}
-* [[Resource Reservation Protocol|RSVP]] is assigned port 363 see {{IETF RFC|2205}}
-* [[Naphthalene]] is dealt with in PIM (Poisons Information Monograph) 363
-* Form 363 is the [[Companies House]] annual return filed in the [[United Kingdom]].
-==Products==
-* The 363 is model of mid-size [[cruiser]].{{Citation needed|date=May 2015}}
 ==References==
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 [[Category:Integers]]
+{{Num-stub}}