OFFSET
1,3
REFERENCES
J.-P. Serre, A Course in Arithmetic, Springer-Verlag, 1973, Chap. VII, Section 4., p. 93.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: (Sum_{k>0} k^3 * x^k / (1 - x^k))^2.
a(n) = (sigma_7(n) - sigma_3(n)) / 120.
G.f.: ((Q(x) - 1) / 240)^2 where Q() is a Ramanujan Eisenstein series.
EXAMPLE
G.f. = x^2 + 18*x^3 + 137*x^4 + 650*x^5 + 2350*x^6 + 6860*x^7 + 17609*x^8 + ...
MAPLE
with(numtheory); f:=n->add( sigma[3](k)*sigma[3](n-k), k=1..n-1);
MATHEMATICA
a[ n_] := If[ n < 1, 0, (DivisorSigma[ 7, n] - DivisorSigma[ 3, n]) / 120]; (* Michael Somos, Oct 08 2017 *)
PROG
(PARI) {a(n) = if( n<1, 0, (sigma(n, 7) - sigma(n, 3)) / 120)};
(PARI) {a(n) = if( n<1, 0, sum(m=1, n-1, sigma(m, 3) * sigma(n-m, 3)))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 13 2003
STATUS
approved