A123621 Greatest k <= n/2 such that n divides binomial(n,k).

0, 1, 1, 1, 2, 1, 3, 3, 4, 4, 5, 6, 6, 5, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 28, 29, 29, 30, 29, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37

Offset

1,5

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Binomial Coefficient

Index entries for triangles and arrays related to Pascal's triangle

Formula

A007318(n,a(n)) mod n = 0.

a(p) = floor(p/2) for primes p.

Mathematica

gk[n_]:=Module[{k=Floor[n/2]}, While[!Divisible[Binomial[n, k], n], k--]; k]; Array[gk, 80] (* Harvey P. Dale, Nov 22 2013 *)

Prog

(PARI) a(n) = if (n>1, my(k=n\2); while (binomial(n, k) % n, k--); k, 0); \\ Michel Marcus, Nov 06 2022

Crossrefs

Sequence in context: A097357 A342016 A360923 * A370592 A151662 A049786

Adjacent sequences: A123618 A123619 A123620 * A123622 A123623 A123624

Keyword

nonn

Author

Reinhard Zumkeller, Oct 03 2006

Status

approved