

A013937


a(n) = Sum_{k=1..n} floor(n/k^3).


4



0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80, 81, 82
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


LINKS

Table of n, a(n) for n=0..71.
Benoit Cloitre, Plot of (a(n)zeta(3)*n)/n^(1/3)zeta(1/3)


FORMULA

a(n) = a(n1)+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

A013937:=n>add(floor(n/k^3), k=1..n); seq(A013937(n), n=0..100); # Wesley Ivan Hurt, Feb 15 2014


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

Cf. A005187, A006218, A011371, A013936, A013939 for similar sequences.
Sequence in context: A248375 A037477 A277050 * A118065 A020661 A284837
Adjacent sequences: A013934 A013935 A013936 * A013938 A013939 A013940


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Henri Lifchitz


EXTENSIONS

More terms from Henry Bottomley, Jul 03 2001


STATUS

approved



