OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
FORMULA
Dirichlet g.f.: zeta(x-1)*zeta(x-4).
Multiplicative with a(p^e) = (p^(4e+7) - (p^3+p^2+p+1)*p^(e+1) + p^2+p+1)/(p^7 - (p^3+p^2+p+1)*p + p^2+p+1). - Mitch Harris, Jun 27 2005
L.g.f.: -log(Product_{k>=1} (1 - x^k)^sigma_3(k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 23 2018
Sum_{k=1..n} a(k) ~ Pi^4 * n^5 / 450. - Vaclav Kotesovec, Feb 16 2020
MATHEMATICA
f[p_, e_] := (1 + p + p^2 - p^(e+1) - p^(e+2) - p^(e+3) - p^(e+4) + p^(4*e+7))/(1 - p^3 - p^4 + p^7); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Oct 03 2023 *)
PROG
(PARI)N=66; x='x+O('x^N); /* that many terms */
c=sum(j=1, N, j*x^j);
t=log(1/prod(j=1, N, eta(x^(j))^(j^3)));
Vec(serconvol(t, c)) /* show terms */
/* Joerg Arndt, May 03 2008 */
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved