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 A309556 #18 Feb 16 2025 08:33:55
%S A309556 52781,782957,1395353,2602439
%N A309556 Composite numbers m such that m divides Sum_{k=1..m-1} (lcm(1,2,...,(m-1)) / k)^2.
%C A309556 Composites m such that m | H_2(m-1) * lcm(1^2,2^2,...,(m-1)^2), where H_2(m) = 1/1^2 + 1/2^2 + ... + 1/m^2.
%C A309556 By Wolstenholme's theorem, if p > 3 is a prime, then p divides the numerator of H_2(p-1) and thus H_2(p-1) * lcm(1,2^2,...,(p-1)^2) == 0 (mod p). This sequence is formed by the pseudoprimes that are solutions of this congruence.
%C A309556 a(5) > 10^7 if it exists.
%H A309556 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WolstenholmesTheorem.html">Wolstenholme's Theorem</a>.
%H A309556 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wolstenholme%27s_theorem">Wolstenholme's theorem</a>.
%t A309556 s = 0; c = 1; n = 1; seq = {}; Do[s += 1/n^2; c = LCM[c, n^2]; n++; If[CompositeQ[n] && Divisible[s*c, n], AppendTo[seq, n]], {2 * 10^6}]; seq
%Y A309556 Cf. A007406, A007407, A025529 (see our comment), A051418.
%K A309556 nonn,bref,more
%O A309556 1,1
%A A309556 _Amiram Eldar_ and _Thomas Ordowski_, Aug 07 2019