A073706 a(n) = Sum_{ d divides n } (n/d)^(3d).

1, 9, 28, 129, 126, 1458, 344, 8705, 20413, 49394, 1332, 1104114, 2198, 2217546, 16305408, 33820673, 4914, 532253187, 6860, 2392632274, 10500716072, 8591716802, 12168, 422182489826, 30517593751, 549760658274, 7625984925160

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..2096

Formula

G.f.: Sum_{n>=1} -log(1 - (n^3)*x^n)/n = Sum_{n>=1} a(n) x^n/n.

G.f.: Sum_{k>=1} k^3*x^k/(1-k^3*x^k). - Benoit Cloitre, Apr 21 2003

Example

a(10) = (10/1)^(3*1) +(10/2)^(3*2) +(10/5)^(3*5) +(10/10)^(3*10) = 49394 because positive divisors of 10 are 1, 2, 5, 10.

Mathematica

Table[Total[Quotient[n, x = Divisors[n]]^(3*x)], {n, 27}] (* Jayanta Basu, Jul 08 2013 *)

Crossrefs

Sum_{ d divides n } (n/d)^(k*d): A000005 (k=0), A055225 (k=1), A073705 (k=2), this sequence (k=3).

Sequence in context: A085292 A198059 A181090 * A226976 A042501 A271185

Adjacent sequences: A073703 A073704 A073705 * A073707 A073708 A073709

Keyword

easy,nonn

Author

Paul D. Hanna, Aug 04 2002

Status

approved