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Numbers k such that A183097(k) > 2*k.
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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