A349111 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).

1, 4, 8, 16, 32, 64, 128, 144, 216, 432, 864, 1296, 1728, 2592, 5184, 10368, 15552, 31104, 54000, 108000, 162000, 216000, 324000, 648000, 1296000, 1944000, 3240000, 3888000, 6480000, 9720000, 19440000, 38880000, 58320000, 74088000, 111132000, 222264000, 444528000, 666792000

Offset: 1

Author

Amiram Eldar, Nov 08 2021

Keywords

• nonn

Comments

The corresponding record values are 1, 5/4, 13/8, 29/16, 61/32, 125/64, ...

The least term k with psigma(k)/k > m, for m = 2, 3, ..., is 144, 54000, 666792000, ...

Crossrefs

Subsequence of A349112.

Cf. A005934, A183097.

Similar sequences: A002110 (unitary), A037992 (infinitary), A061742, A292984, A329882, A348273.

Programs

Mathematica

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