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A081372 a(n) is the number of j from 1 to n such that binomial(n,j) is divisible by j.

%I A081372 #16 Mar 20 2024 05:10:37
%S A081372 1,1,1,2,2,1,1,2,4,3,3,3,3,1,1,3,3,5,5,4,3,1,1,2,4,2,6,7,7,2,2,8,7,6,
%T A081372 5,6,6,4,2,4,4,2,2,2,4,2,2,4,8,12,9,8,8,12,10,12,11,8,8,6,6,3,4,14,12,
%U A081372 9,9,9,7,4,4,7,7,6,9,11,10,4,4,6,17,15,15,11,9,6,6,9,9,6,5,6,5,2,1,4,4,9,12
%N A081372 a(n) is the number of j from 1 to n such that binomial(n,j) is divisible by j.
%C A081372 a(n) is the number of 0's in row n of A081371.
%H A081372 Robert Israel, <a href="/A081372/b081372.txt">Table of n, a(n) for n = 1..10000</a>
%e A081372 n=10: C(10,j) mod j, j=1..10, is {0,1,0,2,2,0,1,5,1,1} includes 3 zeros, so a(10)=3.
%p A081372 f:= n -> numboccur(0, map(j -> binomial(n,j) mod j, [$1..n])):
%p A081372 map(f, [$1..100]); # _Robert Israel_, Mar 19 2024
%t A081372 Flatten[Table[Count[Table[Mod[Binomial[n, j], j], {j, 1, n}], 0], {n, 1, 256}], 1]
%Y A081372 Cf. A007318, A081371.
%K A081372 nonn,look
%O A081372 1,4
%A A081372 _Labos Elemer_, Mar 21 2003
%E A081372 Definition edited by _Robert Israel_, Mar 19 2024