A081543 G.f.: Sum_{k >= 1} x^k/(1-x^k)^(k+1).

1, 3, 4, 8, 6, 17, 8, 24, 20, 32, 12, 76, 14, 51, 72, 97, 18, 158, 20, 213, 142, 101, 24, 491, 152, 132, 248, 479, 30, 915, 32, 681, 398, 206, 828, 1859, 38, 249, 600, 2560, 42, 2692, 44, 1686, 2864, 347, 48, 6166, 1766, 3405, 1192, 2811, 54, 6796, 4424, 9987

Offset: 1

Author

Benoit Cloitre, Apr 21 2003

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..999 from Harvey P. Dale)

Crossrefs

Cf. A157019.

Programs

Mathematica

With[{nn=50},CoefficientList[Series[Sum[x^k/(1-x^k)^(k+1),{k,nn}],{x,0,nn}],x]] (* Harvey P. Dale, May 28 2017 *)

PARI

a(n)=if(n<1,0,polcoeff(sum(k=1,n,1/(1-x^k)^k,x*O(x^(n^2))),n))

Formula

If p is prime then a(p)=p+1.

a(n) = Sum_{d|n} binomial(d-1+n/d,d). - R. J. Mathar, Feb 21 2009

Extensions

Description corrected by Vladeta Jovovic, Aug 22 2003

Corrected offset R. J. Mathar, Feb 21 2009