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 A276485 #16 Feb 16 2025 08:33:36 %S A276485 1,5,251,22369,806108207,47464376609,774879868932307123, %T A276485 248886558707571775009601,4106541588424891370931874221019, %U A276485 413520574906423083987893722912609,7429165883912264897181708263009894640627544300697 %N A276485 Numerator of Sum_{k=1..n} 1/k^n. %C A276485 Also numerators 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 A276485 Sum_{k>=1} 1/k^n = zeta(n). %H A276485 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a> %H A276485 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a> %H A276485 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HurwitzZetaFunction.html">Hurwitz Zeta Function</a> %e A276485 1, 5/4, 251/216, 22369/20736, 806108207/777600000, 47464376609/46656000000, 774879868932307123/768464444160000000, ... %e A276485 a(3) = 251, because 1/1^3 + 1/2^3 + 1/3^3 = 251/216. %t A276485 Table[Numerator[HarmonicNumber[n, n]], {n, 1, 11}] %o A276485 (PARI) a(n) = numerator(sum(k=1, n, 1/k^n)); \\ _Michel Marcus_, Sep 06 2016 %Y A276485 Cf. A001008, A002805, A007406, A007407, A031971, A276487 (denominators). %K A276485 nonn,frac %O A276485 1,2 %A A276485 _Ilya Gutkovskiy_, Sep 05 2016