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 A126563 #22 Jul 10 2025 09:14:14
%S A126563 119,735,5145,36015,252105,1764735,12353145
%N A126563 Numbers k such that the ratio of A117731(k) and A082687(k) is composite.
%C A126563 a(1) = 7*17, a(2) = 3*5*7^2, a(3) = 3*5*7^3.
%C A126563 Corresponding composite terms in A125741 are {119, 49, 49, 49, 49, 49, 49, ...}.
%C A126563 A125741(n) is composite for n = {7, 16, 36, 91, 226, 510, 1131, ...}.
%H A126563 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>.
%H A126563 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HilbertMatrix.html">Hilbert Matrix</a>.
%t A126563 h=0; Do[ h=h+1/(n+1)/(2n+1); f=Numerator[n*h]; g=Numerator[h]; If[ !Equal[f, g] && !PrimeQ[f/g], Print[ {n, f/g, FactorInteger[n], FactorInteger[f/g]} ] ], {n, 1, 10000} ]
%o A126563 (PARI) f(n) = sum(k=1, n, 1/(n+k));
%o A126563 isok(k) = my(fk = f(k), q = numerator(k*fk)/numerator(fk)); (q!=1) && !isprime(q); \\ _Michel Marcus_, Mar 08 2023
%Y A126563 Cf. A082687, A117731, A125581, A125740, A125741, A126196, A126197.
%K A126563 nonn,hard,more
%O A126563 1,1
%A A126563 _Alexander Adamchuk_, Mar 12 2007, Jun 09 2007
%E A126563 Edited by _Max Alekseyev_, Jul 12 2019
%E A126563 a(5)-a(7) from _Jinyuan Wang_, Jul 10 2025