|
|
A082245
|
|
Sum of (n-1)-th powers of divisors of n.
|
|
8
|
|
|
1, 3, 10, 73, 626, 8052, 117650, 2113665, 43053283, 1001953638, 25937424602, 743375541244, 23298085122482, 793811662272744, 29192932133689220, 1152956690052710401, 48661191875666868482, 2185928253847184914509
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) = t(n,n-1), t as defined in A082771;
|
|
LINKS
|
|
|
FORMULA
|
L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^(1/k^2)) = Sum_{k>=1} a(k)*x^k/k. - Seiichi Manyama, Jun 23 2019
|
|
EXAMPLE
|
a(6) = 1^5 + 2^5 + 3^5 + 6^5 = 1 + 32 + 243 + 7776 = 8052.
|
|
MATHEMATICA
|
Table[Total[Divisors[n]^(n-1)], {n, 18}] (* T. D. Noe, Oct 25 2006 *)
Table[DivisorSigma[n-1, n], {n, 1, 20}] (* G. C. Greubel, Nov 02 2018 *)
|
|
PROG
|
(Sage) [sigma(n, (n-1))for n in range(1, 19)] # Zerinvary Lajos, Jun 04 2009
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^(1/k^2))))) \\ Seiichi Manyama, Jun 23 2019
(Magma) [DivisorSigma(n-1, n): n in [1..20]]; // G. C. Greubel, Nov 02 2018
|
|
CROSSREFS
|
Cf. A023887, A000005, A000203, A001157, A001158, A001159, A001160, A013954, A013955, A013956, A013957, A013958
Cf. A013959, A013960, A013961, A013962, A013963, A013964, A013965, A013966, A013967, A013968, A013969, A013970
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|