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.
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 *)
Join[{0}, Table[Count[Table[Binomial[n, k], {k, 0, n}], _?(Mod[#, n]==0&)], {n, 100}]] (* Harvey P. Dale, Sep 20 2024 *)
PROG
(Haskell)
a020475 n = a020475_list !! n
a020475_list = 0 : map (sum . map (0 ^)) (tail a053200_tabl)
-- Reinhard Zumkeller, Jan 24 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from T. D. Noe, Feb 23 2006
STATUS
approved