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%I #6 Nov 08 2021 04:29:28
%S 1,4,8,16,32,64,128,144,216,432,864,1296,1728,2592,5184,10368,15552,
%T 31104,54000,108000,162000,216000,324000,648000,1296000,1944000,
%U 3240000,3888000,6480000,9720000,19440000,38880000,58320000,74088000,111132000,222264000,444528000,666792000
%N Powerful superabundant numbers: numbers m such that psigma(m)/m > psigma(k)/k for all k < m, where psigma(k) is the sum of powerful divisors of k (A183097).
%C The corresponding record values are 1, 5/4, 13/8, 29/16, 61/32, 125/64, ...
%C The least term k with psigma(k)/k > m, for m = 2, 3, ..., is 144, 54000, 666792000, ...
%t f[p_,e_] := (p^(e+1)-1)/(p-1) - p; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; seq = {}; rm = 0; Do[r1 = s[n]/n; If[r1 > rm, rm = r1; AppendTo[seq, n]], {n, 1, 10^6}]; seq
%Y Subsequence of A349112.
%Y Cf. A005934, A183097.
%Y Similar sequences: A002110 (unitary), A037992 (infinitary), A061742, A292984, A329882, A348273.
%K nonn
%O 1,2
%A _Amiram Eldar_, Nov 08 2021
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