A349112 Powerful highly abundant numbers: numbers m such that psigma(m) > psigma(k) for all k < m, where psigma(k) is the sum of powerful divisors of k (A183097).

1, 4, 8, 16, 27, 32, 64, 72, 108, 128, 144, 200, 216, 256, 288, 392, 400, 432, 576, 648, 800, 864, 1152, 1296, 1728, 1944, 2304, 2592, 3456, 3888, 5184, 6912, 7776, 10000, 10368, 11664, 13824, 15552, 20000, 20736, 23328, 27000, 27648, 31104, 34992, 40000, 41472

Offset: 1

Author

Amiram Eldar, Nov 08 2021

Keywords

• nonn

Comments

The corresponding record values are 1, 5, 13, 29, 37, 61, 125, 130, 185, 253, ...

Examples

			The first 8 terms of A183097 are 1, 1, 1, 5, 1, 1, 1 and 13. The record values, 1, 5 and 13, occur at 1, 4 and 8, the first 3 terms of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..287 (terms below 10^10)

Crossrefs

A349111 is a subsequence.

Cf. A005934, A183097.

Similar sequences: A285614, A292983, A327634, A328134, A329883, A348272.

Programs

Mathematica

f[p_,e_] := (p^(e+1)-1)/(p-1) - p; s[1] = 1; s[n_] := Times @@ f @@@FactorInteger[n]; seq = {}; sm = 0; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq