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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).
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%I #11 May 18 2023 10:40:46

%S 1,4,8,16,27,32,64,72,108,128,144,200,216,256,288,392,400,432,576,648,

%T 800,864,1152,1296,1728,1944,2304,2592,3456,3888,5184,6912,7776,10000,

%U 10368,11664,13824,15552,20000,20736,23328,27000,27648,31104,34992,40000,41472

%N 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).

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

%H Amiram Eldar, <a href="/A349112/b349112.txt">Table of n, a(n) for n = 1..287</a> (terms below 10^10)

%e 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.

%t 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

%Y A349111 is a subsequence.

%Y Cf. A005934, A183097.

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 08 2021