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 A379922 #8 Jan 06 2025 10:55:29
%S A379922 1,2,3,42,329,633,1039,5689,26621,39245,1101875,1216075,40088584,
%T A379922 67244920,104332211,549673265,777631064,19879301756
%N A379922 Numbers m that divide the alternating sum Sum_{k=1..m} (-1)^(k+1) * sigma_2(k).
%C A379922 Numbers m such that m | A379921(m).
%C A379922 The corresponding quotients, A379921(m)/m, are -1, 2, -2, 120, 5228, ... (see the link for more values).
%C A379922 a(19) > 5*10^10, if it exists.
%H A379922 Amiram Eldar, <a href="/A379922/a379922.txt">Table of n, a(n), A379921(a(n))/a(n) for n = 1..18</a>.
%t A379922 With[{m = 40000}, Position[Accumulate[Table[(-1)^n * DivisorSigma[2, n], {n, 1, m}]]/Range[m], _?IntegerQ] // Flatten]
%o A379922 (PARI) list(lim) = my(s = 0); for(k = 1, lim, s += (-1)^k * sigma(k, 2); if(!(s % k), print1(k, ", ")));
%Y A379922 Cf. A001157 (sigma_2), A379921.
%Y A379922 Similar sequences: A050226, A048290, A056550, A064605, A067929, A067931, A379923, A379924.
%K A379922 nonn,more
%O A379922 1,2
%A A379922 _Amiram Eldar_, Jan 06 2025