OFFSET
1,64
COMMENTS
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Cubic Number.
FORMULA
a(n) = 1/n*Sum_{k=1..n} (b(k)-1)*a(n-k), a(0) = 1, where b(k) is sum of cube divisors of k. - Vladeta Jovovic, Nov 20 2002
From Vaclav Kotesovec, Jan 05 2017: (Start)
a(n) ~ exp(4*(Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4) / 3^(3/2)) * (Gamma(1/3) * Zeta(4/3))^(3/2) / (8 * 3^(5/2) * Pi^2 * n^2).
(End)
EXAMPLE
a(160)=4: 160 = 20*2^3 = 4^3+12*2^3 = 2*4^3+4*2^3 = 5^3+3^3+2^3.
MATHEMATICA
nmax = 105; CoefficientList[Series[Product[1/(1 - x^(k^3)), {k, 1, nmax}], {x, 0, nmax}], x] // Differences (* Jean-François Alcover, Mar 01 2019, after Vaclav Kotesovec *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 19 2002
STATUS
approved