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

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, 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, 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

Offset: 1

Author

Labos Elemer, Mar 21 2003

Keywords

• nonn
• look

Comments

a(n) is the number of 0's in row n of A081371.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007318, A081371.

Programs

Maple

f:= n -> numboccur(0, map(j -> binomial(n,j) mod j, [$1..n])):
map(f, [$1..100]); # Robert Israel, Mar 19 2024

Mathematica

Flatten[Table[Count[Table[Mod[Binomial[n, j], j], {j, 1, n}], 0], {n, 1, 256}], 1]

Extensions

Definition edited by Robert Israel, Mar 19 2024