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%I #12 Nov 07 2021 09:49:40
%S 144,216,288,432,576,648,864,1152,1296,1600,1728,1944,2000,2304,2592,
%T 3200,3456,3600,3888,4000,4608,5000,5184,5400,5488,5832,6272,6400,
%U 6912,7056,7200,7776,8000,9000,9216,10000,10368,10584,10800,10976,11664,12544,12800,13500
%N Numbers k such that A183097(k) > 2*k.
%C The least odd term is a(934) = A349065(1) = 3472875.
%C Not all the terms are powerful. E.g., (prime(44)#)^3/4 and (prime(22)#)^6/32 are nonpowerful terms. What is the least nonpowerful term?
%H Amiram Eldar, <a href="/A349064/b349064.txt">Table of n, a(n) for n = 1..10000</a>
%e 144 is a term since A183097(144) = 290 > 2*144 = 288.
%t f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - p; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := s[n] > 2*n; Select[Range[15000], q]
%o (PARI) isok(k) = sumdiv(k, d, ispowerful(d)*d) > 2*k; \\ _Michel Marcus_, Nov 07 2021
%Y Subsequence of A005101.
%Y A349065 is a subsequence.
%Y Cf. A001694, A183097.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 07 2021