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 A276487 #17 Feb 16 2025 08:33:36 %S A276487 1,4,216,20736,777600000,46656000000,768464444160000000, %T A276487 247875891108249600000000,4098310578334288576512000000000, %U A276487 413109706296096288512409600000000,7425496288284402957501110551810198732800000000000 %N A276487 Denominator of Sum_{k=1..n} 1/k^n. %C A276487 Also denominator of zeta(n) - Hurwitz zeta(n,n+1), where zeta(s) is the Riemann zeta function and Hurwitz zeta(s,a) is the Hurwitz zeta function. %C A276487 Sum_{k>=1} 1/k^n = zeta(n). %H A276487 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a> %H A276487 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a> %H A276487 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HurwitzZetaFunction.html">Hurwitz Zeta Function</a> %e A276487 1, 5/4, 251/216, 22369/20736, 806108207/777600000, 47464376609/46656000000, 774879868932307123/768464444160000000, ... %e A276487 a(3) = 216, because 1/1^3 + 1/2^3 + 1/3^3 = 251/216. %p A276487 A276487:=n->denom(add(1/k^n, k=1..n)): seq(A276487(n), n=1..12); # _Wesley Ivan Hurt_, Sep 07 2016 %t A276487 Table[Denominator[HarmonicNumber[n, n]], {n, 1, 11}] %o A276487 (PARI) a(n) = denominator(sum(k=1, n, 1/k^n)); \\ _Michel Marcus_, Sep 06 2016 %Y A276487 Cf. A001008, A002805, A007406, A007407, A031971, A276485 (numerators). %K A276487 nonn,frac %O A276487 1,2 %A A276487 _Ilya Gutkovskiy_, Sep 05 2016