cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A013938 a(n) = Sum_{k=1..n} floor(n/k^4).

This page as a plain text file.
%I A013938 #21 May 26 2021 13:03:51
%S A013938 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,
%T A013938 28,29,30,31,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,52,
%U A013938 53,54,55,56,57,58,59,60,61,62,63,64,65,66,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,85,87
%N A013938 a(n) = Sum_{k=1..n} floor(n/k^4).
%H A013938 Seiichi Manyama, <a href="/A013938/b013938.txt">Table of n, a(n) for n = 1..10000</a>
%F A013938 G.f.: (1/(1 - x))*Sum_{k>=1} x^(k^4)/(1 - x^(k^4)). - _Ilya Gutkovskiy_, Feb 11 2017
%F A013938 a(n) ~ zeta(4)*n = Pi^4*n/90. - _Vaclav Kotesovec_, Oct 12 2019
%t A013938 Table[Sum[Floor[n/k^4], {k, 1, n}], {n, 1, 100}] (* _Vaclav Kotesovec_, Oct 12 2019 *)
%o A013938 (PARI) a(n) = sum(k=1, n, n\k^4); \\ _Michel Marcus_, Feb 11 2017
%Y A013938 Cf. A013936, A013937.
%K A013938 nonn
%O A013938 1,2
%A A013938 _N. J. A. Sloane_, _Henri Lifchitz_