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 A379924 #14 Apr 26 2025 05:31:27
%S A379924 1,2,9,54,101,178,189,2071,3070,9171,11450,12794,21405,27553,35285,
%T A379924 251974,2069863,2395894,155931488,387586437,758519827,1202435693,
%U A379924 9859113494,42703260442
%N A379924 Numbers m that divide the alternating sum Sum_{k=1..m} (-1)^(k+1) * usigma(k).
%C A379924 Numbers m such that m | A370898(m).
%C A379924 The corresponding quotients, A370898(m)/m, are -1, 1, 0, 6, 9, ... (see the link for more values).
%C A379924 a(25) > 5*10^10, if it exists.
%H A379924 Amiram Eldar, <a href="/A379924/a379924.txt">Table of n, a(n), A370898(a(n))/a(n) for n = 1..24</a>.
%t A379924 usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); usigma[1] = 1; With[{m = 260000}, Position[Accumulate[Table[(-1)^n * usigma[n], {n, 1, m}]]/Range[m], _?IntegerQ] // Flatten]
%o A379924 (PARI) usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]); }
%o A379924 list(lim) = my(s = 0); for(k = 1, lim, s += (-1)^k * usigma(k); if(!(s % k), print1(k, ", ")));
%Y A379924 Cf. A034448 (usigma), A370898.
%Y A379924 Similar sequences: A050226, A048290, A056550, A064605, A067929, A067931, A379922, A379923.
%K A379924 nonn,more
%O A379924 1,2
%A A379924 _Amiram Eldar_, Jan 06 2025