A177501 The number of entries in row n of table A174625 which are multiples of n.

1, 1, 1, 1, 2, 1, 3, 2, 3, 2, 5, 2, 6, 4, 4, 5, 8, 4, 9, 4, 6, 6, 11, 4, 10, 8, 10, 7, 14, 6, 15, 11, 10, 12, 12, 8, 18, 12, 13, 10, 20, 8, 21, 12, 15, 16, 23, 13, 21, 16, 19, 15, 26, 15, 21, 15, 21, 22, 29, 13, 30, 26, 21, 24, 25, 18, 33, 21, 25, 19, 35, 18, 36, 26, 24, 23, 31, 19, 39, 23

Offset: 1

Author

Vladimir Shevelev, May 10 2010

Keywords

• nonn

Comments

n is prime iff a(n) = floor(n/2).

For n >= 2, a(n) is the number of integers of the form binomial(n-k-1, k-1)/k, k=1..floor(n/2). - Vladimir Shevelev, Aug 18 2013

Examples

			In the fifth row, 5 and 5 are both multiples of 5, so a(5)=2.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A174625, A221533.

Programs

Mathematica

p[0]:=0; p[1]:=2; p[n_]:=p[n]=Expand[p[n-1] +x p[n-2]+1]; Flatten[{1,Table[Count[CoefficientList[p[n]/(n+1) ,x],Integer],{n,50}]}] (* _Peter J. C. Moses, Aug 20 2013 *)

Formula

For n >= 2, a(n) >= A000010(n)/2. Equality holds when n is odd prime.

Extensions

Definition shortened, more terms added by R. J. Mathar, Nov 01 2010