126 (number)

Source: Wikipedia, the free encyclopedia.
← 125 126 127 →
Cardinalone hundred twenty-six
Ordinal126th
(one hundred twenty-sixth)
Factorization2 × 32 × 7
Divisors1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Greek numeralΡΚϚ´
Roman numeralCXXVI
Binary11111102
Ternary112003
Senary3306
Octal1768
DuodecimalA612
Hexadecimal7E16

126 (one hundred [and] twenty-six) is the natural number following 125 and preceding 127.

In mathematics

As the binomial coefficient , 126 is a

Pascal's Triangle, it is a pentatope number.[1][2] 126 is a sum of two cubes, and since 125 + 1 is σ3(5), 126 is the fifth value of the sum of cubed divisors function.[3][4]

126 is the fifth -perfect Granville number, and the third such not to be a perfect number. Also, it is known to be the smallest Granville number with three distinct prime factors, and perhaps the only such Granville number.[5]

126 is a

pentagonal pyramidal number and a decagonal number.[6][7] 126 is also the different number of ways to partition a decagon into even polygons by diagonals, and the number of crossing points among the diagonals of a regular nonagon.[8][9]

There are exactly 126

binary strings of length seven that are not repetitions of a shorter string, and 126 different semigroups on four elements (up to isomorphism and reversal).[10][11]

There are exactly 126 positive integers that are not solutions of the equation

where a, b, c, and d must themselves all be positive integers.[12]

126 is the number of

root vectors of simple Lie group E7
.

In physics

126 is the seventh

half life that its existence could be detected.[13]

See also

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A001405 (Central binomial coefficients)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. See also OEIS:A001700 for the odd central binomial coefficients.
  2. ISBN 9789814355483; Sloane, N. J. A. (ed.). "Sequence A000332 (Binomial coefficients binomial(n,4))". The On-Line Encyclopedia of Integer Sequences
    . OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A003325 (Numbers that are the sum of 2 positive cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A001158 (sigma_3(n): sum of cubes of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. OCLC 317778112
    .
  6. ^ Deza & Deza (2012), pp. 93, 211. Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Deza & Deza (2012), pp. 2–3 and 6; Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A003168 (Number of blobs with 2n+1 edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A006561 (Number of intersections of diagonals in the interior of regular n-gon)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A027375 (Number of aperiodic binary strings of length n; also number of binary sequences with primitive period n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A001423 (Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A027566 (Number of numbers not of form k_1 k_2 .. k_n (1/k_1 + .. + 1/k_n), k_i >= 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.. See OEIS:A027563 for the list of these 126 numbers.
  13. ISBN 9780199605637
Retrieved from "https://en.wikipedia.org/w/index.php?title=126_(number)&oldid=1187741301"