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 A120347 #16 Feb 16 2025 08:33:01
%S A120347 1,9,1393,257875,47463376609,940908897061,972213062238348973121,
%T A120347 7727182467755471289426059,10338014371627802833957102351534201,
%U A120347 26038773205374138944970092886340352227,205885410277133543091182509665217407908365393153956577
%N A120347 Numerator of Sum_{k=1..n-1} 1/k^n.
%C A120347 Prime p>2 divides a(p). p^3 divides a(p) for prime p>3. p divides a((p+1)/2) for prime p = {7,11,17,19,23,31,41,43,47,59,67,71,73,79,83,89,97,103,...} = all primes excluding 2 and 3 from A045323[n] Primes congruent to {1, 2, 3, 7} mod 8.
%C A120347 a(n) = Numerator( H(n-1,n) ), where H(k,r) = Sum_{i=1..k} 1/i^r is the generalized harmonic number.
%H A120347 Vincenzo Librandi, <a href="/A120347/b120347.txt">Table of n, a(n) for n = 2..49</a>
%H A120347 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WolstenholmesTheorem.html">Wolstenholme's Theorem</a>
%H A120347 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%F A120347 a(n) = Numerator(Sum_{k=1..n-1} 1/k^n). a(n) = Numerator[Zeta[n] - Zeta[n,n]].
%t A120347 Table[Numerator[Sum[1/k^n,{k,1,n-1}]],{n,2,15}]
%Y A120347 Cf. A045323, A120289, A120352 (a(prime(n))), A119722 (a(prime(n))/prime(n)^3).
%K A120347 nonn,frac
%O A120347 2,2
%A A120347 _Alexander Adamchuk_, Aug 16 2006, Oct 31 2006