OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Benoit Cloitre, Plot of (a(n)-zeta(3)*n)/n^(1/3)-zeta(1/3)
FORMULA
a(n) = a(n-1)+A061704(n). a(n) = Sum_{k=1..n} floor((n/k)^(1/3)) with asymptotic formula: a(n) = zeta(3)*n+zeta(1/3)*n^(1/3)+O(n^theta) where theta<1/3 and we conjecture that theta=1/4+epsilon is the best possible choice. - Benoit Cloitre, Nov 05 2012
G.f.: (1/(1 - x))*Sum_{k>=1} x^(k^3)/(1 - x^(k^3)). - Ilya Gutkovskiy, Feb 11 2017
EXAMPLE
a(36) = [36/1]+[36/8]+[36/27]+[36/64]+... = 36+4+1+0+... = 41.
MAPLE
MATHEMATICA
Table[Sum[Floor[n/k^3], {k, n}], {n, 0, 100}] (* Wesley Ivan Hurt, Feb 15 2014 *)
PROG
(PARI) a(n)=sum(k=1, ceil(n^(1/3)), n\k^3) /*Benoit Cloitre, Nov 05 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Henry Bottomley, Jul 03 2001
STATUS
approved