276 (number)

276 (two hundred [and] seventy-six) is the natural number following 275 and preceding 277.

← 275 276 277 →
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Cardinaltwo hundred seventy-six
Ordinal276th
(two hundred seventy-sixth)
Factorization22 × 3 × 23
Greek numeralΣΟϚ´
Roman numeralCCLXXVI
Binary1000101002
Ternary1010203
Octal4248
Duodecimal1B012
Hexadecimal11416

In mathematics

276 is the sum of 3 consecutive fifth powers (276 = 15 + 25 + 35).[1] As a figurate number it is a triangular number, a hexagonal number, and a centered pentagonal number, the third number after 1 and 6 to have this combination of properties.[2]

276 is the size of the largest set of equiangular lines in 23 dimensions. The maximal set of such lines, derived from the Leech lattice, provides the highest dimension in which the "Gerzon bound" of is known to be attained; its symmetry group is the third Conway group, Co3.[3][4]

276 is the smallest number for which it is not known if the corresponding aliquot sequence either terminates or ends in a repeating cycle.[5]

In other fields

In the Christian calendar, there are 276 days from the Annunciation on March 25 to Christmas on December 25, a number considered significant by some authors.[6]

See also

References
  1. Sloane, N. J. A. (ed.). "Sequence A000539 (Sum of 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. Sloane, N. J. A. (ed.). "Sequence A254628 (Triangular numbers that are also centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. Sloane, N. J. A. (ed.). "Sequence A002853 (Maximal size of a set of equiangular lines in n dimensions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. Lemmens, P. W. H.; Seidel, J. J. (1973). "Equiangular lines". Journal of Algebra. 24 (3): 494–512. doi:10.1016/B978-0-12-189420-7.50017-7.
  5. Sloane, N. J. A. (ed.). "Sequence A131884 (Numbers conjectured to have an infinite, aperiodic, aliquot sequence.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. Howlett, David (January 2002). "A miracle of Maedóc". Peritia. 16: 85–93. doi:10.1484/j.peri.3.479.
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