A020475 a(n) is the number of k for which C(n,k) is divisible by n.

0, 2, 1, 2, 2, 4, 2, 6, 4, 6, 6, 10, 5, 12, 6, 8, 8, 16, 10, 18, 10, 14, 14, 22, 10, 20, 18, 18, 14, 28, 11, 30, 16, 26, 30, 26, 22, 36, 30, 30, 22, 40, 20, 42, 26, 26, 30, 46, 20, 42, 34, 32, 34, 52, 26, 46, 33, 50, 42, 58, 26, 60, 30, 46, 32, 50, 48, 66, 58, 50, 44, 70, 40, 72, 66, 46, 58

Offset

0,2

Comments

Note that n is prime iff a(n) = n-1. - T. D. Noe, Feb 23 2006

a(n) >= phi(n) (cf. Robbins). - Michel Marcus, Oct 31 2012

For n > 0: number of zeros in n-th row of A053200. - Reinhard Zumkeller, Jan 01 2013

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

H. Harborth, Divisibility of binomial coefficients by their row number, The American Mathematical Monthly, Vol. 84, No. 1 (Jan., 1977), pp. 35-37.

N. Robbins, On the number of binomial coefficients which are divisible by their row number, Canad. Math. Bull. 25(1982), 363-365.

N. Robbins, On the number of binomial coefficients which are divisible by their row number. II, Canad. Math. Bull. 28(1985), 481-486.

Formula

a(n) = n + 1 - A007012(n). - T. D. Noe, Feb 23 2006

Mathematica

Table[cnt=0; Do[If[Mod[Binomial[n, k], n]==0, cnt++ ], {k, 0, n}]; cnt, {n, 0, 100}] (* T. D. Noe, Feb 23 2006 *)

Prog

(Haskell)
a020475 n = a020475_list !! n
a020475_list = 0 : map (sum . map (0 ^)) (tail a053200_tabl)
-- Reinhard Zumkeller, Jan 24 2014

Crossrefs

Cf. A007012.

Sequence in context: A339219 A308302 A225530 * A156995 A131183 A346063

Adjacent sequences: A020472 A020473 A020474 * A020476 A020477 A020478

Keyword

nonn

Author

David W. Wilson

Extensions

More terms from T. D. Noe, Feb 23 2006

Status

approved