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 A274564 #27 Jun 09 2025 10:27:31 %S A274564 6,7,8,10,11,15,19,24,33,105,33705,33624064,2199041081344 %N A274564 Numbers k such that sigma(k) == 0 (mod k-9). %e A274564 sigma(10) mod (10 - 9) = 18 mod 1 = 0. %t A274564 k = -9; Select[Range[Abs@k+1, 10^6], Mod[DivisorSigma[1, #], # + k] == 0 &] (* _Vincenzo Librandi_, Jul 06 2016 *) %o A274564 (Magma) [n: n in [10..2*10^6] | SumOfDivisors(n) mod (n-9) eq 0 ]; // _Vincenzo Librandi_, Jul 06 2016 %o A274564 (PARI) isok(k) = (k!=9) && (Mod(sigma(k), k-9) == 0); \\ _Michel Marcus_, May 30 2025 %Y A274564 Contains subsequence A223608. %Y A274564 Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274553, A274554, A274556, A274557, A274558, A274559, A274560, A274561, A274562, A274563, A274565, A274566. %K A274564 nonn,more %O A274564 1,1 %A A274564 _Paolo P. Lava_, Jul 06 2016 %E A274564 a(12)-a(13) from _Giovanni Resta_, Jul 06 2016 %E A274564 Terms 6,7,8 inserted by _Max Alekseyev_, May 29 2025