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

1,5

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A174625, A221533.

Sequence in context: A104481 A078709 A023022 * A330926 A323273 A100677

Adjacent sequences: A177498 A177499 A177500 * A177502 A177503 A177504

Keyword

nonn

Author

Vladimir Shevelev, May 10 2010

Extensions

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

Status

approved