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.

A078837 a(n) = Sum_{k=1..prime(n)-1} floor(k^3/prime(n)).

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%I A078837 #27 Feb 16 2025 08:32:48
%S A078837 0,2,18,60,270,462,1080,1530,2772,5670,6960,11970,16380,18942,24840,
%T A078837 35802,49590,54870,72930,86940,94572,120120,139482,172260,223440,
%U A078837 252450,267852,300510,317790,354312,504000,553410,633420,661710,815850
%N A078837 a(n) = Sum_{k=1..prime(n)-1} floor(k^3/prime(n)).
%H A078837 Harvey P. Dale, <a href="/A078837/b078837.txt">Table of n, a(n) for n = 1..1000</a>
%H A078837 Jean-Christophe Pain, <a href="https://arxiv.org/abs/2303.07934">A prime sum involving Bernoulli numbers</a>, arXiv:2303.07934 [math.HO], 2023. See (22) p. 4.
%H A078837 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A078837 a(n) = (1/4)*(prime(n)-2)*(prime(n)-1)*(prime(n)+1).
%t A078837 Table[(Times@@(Prime[n]+{1,-1,-2}))/4,{n,40}] (* _Harvey P. Dale_, Dec 31 2020 *)
%o A078837 (PARI) a(n) = my(p=prime(n)); sum(k=1, p-1, k^3\p); \\ _Michel Marcus_, Mar 16 2023
%K A078837 nonn
%O A078837 1,2
%A A078837 _Benoit Cloitre_, Dec 08 2002