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.
%I A130681 #13 Feb 16 2025 08:33:06
%S A130681 41361119,126941659254799099843,
%T A130681 201945187495172518712395211386399925751676163316330287629003467281801,
%U A130681 534565103485593943310791656810688803242468895931876288948761507813750601446840308490623197040810555162527973
%N A130681 Sum[ 1/k^(2p-1), {k,1,p-1}] divided by p^3, for prime p>3.
%C A130681 The generalized harmonic number is H(n,m) = Sum[ 1/k^m, {k,1,n} ]. The numerator of H(p-1,2p-1) is divisible by p^3 for prime p>3. Also the numerator of H(p-1,p) is divisible by p^3 for prime p>3. See A119722(n).
%H A130681 Alexander Adamchuk, <a href="/A130681/b130681.txt">Table of n, a(n) for n = 3..10</a>
%H A130681 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WolstenholmesTheorem.html">Wolstenholme's Theorem</a>
%H A130681 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%F A130681 a(n) = Numerator[ Sum[ 1/k^(2*Prime[n]-1), {k,1,Prime[n]-1} ] ] / Prime[n]^3 for n>2.
%F A130681 a(n) = A228426(A000040(n))/A000040(n)^3.
%e A130681 Prime[3] = 5.
%e A130681 a(3) = numerator[ 1 + 1/2^9 + 1/3^9 + 1/4^9 ] / 5^3 = 5170139875/125 = 41361119.
%t A130681 Table[ Numerator[ Sum[ 1/k^(2*Prime[n]-1), {k,1,Prime[n]-1} ] ] / Prime[n]^3, {n,3,10} ]
%o A130681 (PARI) a(n)=p=prime(n);numerator(sum(i=1,p-1,1/i^(2*p-1)))/p^3 \\ _Ralf Stephan_, Nov 10 2013
%Y A130681 Cf. A119722.
%K A130681 frac,nonn
%O A130681 3,1
%A A130681 _Alexander Adamchuk_, Jun 29 2007
%E A130681 Edited by _Ralf Stephan_, Nov 10 2013