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A020475 a(n) is number of k for which C(n,k) is divisible by n. 9
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 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A277891 A102722 A225530 * A156995 A131183 A133770

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

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Last modified October 16 15:27 EDT 2018. Contains 316264 sequences. (Running on oeis4.)