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 A349110 #7 Nov 08 2021 04:29:05 %S A349110 128,729,900,4900,10404,17424,24336,52900,78400,79524,81796,297025, %T A349110 304175,304200,313600,346921,417316,532900,1612900,1656200,1960000, %U A349110 2238016,2464900,3129361,3232804,3334276,3496900,3534400,3992004,6056521,6974881,9245000,10672200 %N A349110 Powerful numbers (A001694) whose sum of aliquot powerful divisors (including 1) is larger than 1 and is also powerful. %C A349110 Numbers k such that A112526(k) = A112526(A183097(k) - k) = 1. %e A349110 128 = 2^7 is a term since it is powerful and the sum of its aliquot powerful divisors, A183097(128) - 128 = 1 + 4 + 8 + 16 + 32 + 64 = 125 = 5^3 is also powerful. %t A349110 powQ[n_] := AllTrue[FactorInteger[n][[;;,2]], # > 1 &]; f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - p; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := powQ[n] && powQ[s[n] - n]; Select[Range[1.1*10^7], q] %o A349110 (PARI) isok(n) = my(s); ispowerful(n) && (s=sumdiv(n, d, if (d<n, d*ispowerful(d)))) && (s>1) && ispowerful(s); \\ _Michel Marcus_, Nov 08 2021 %Y A349110 Cf. A001694, A183097, A349109. %K A349110 nonn %O A349110 1,1 %A A349110 _Amiram Eldar_, Nov 08 2021