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A356420 Integers k such that for some m >= 0, psi(k) = rad(k)^m, where psi(k) = A001615(k) and rad(k) = A007947(k).

%I A356420 #17 Aug 13 2022 15:48:06
%S A356420 1,18,108,648,3888,11250,23328,139968,337500,501126,839808,5038848,
%T A356420 8696754,10125000,30233088,51114852,57177414,181398528,303750000,
%U A356420 573985764,1088391168,2401451388,5018345916,5213714904,6530347008,9112500000,23981814018,26622318750,37883060424
%N A356420 Integers k such that for some m >= 0, psi(k) = rad(k)^m, where psi(k) = A001615(k) and rad(k) = A007947(k).
%C A356420 Inspired by A355045, which has an additional constraint.
%C A356420 If k is a term then k*rad(k) is a term. Hence the sequence is infinite. For example, it contains 18*6^k for k >= 0. - _David A. Corneth_, Aug 07 2022
%t A356420 f[p_, e_] := (p + 1)*p^(e - 1); q[1] = True; q[n_] := IntegerQ @ Log[Times @@ (fct = FactorInteger[n])[[;; , 1]], Times @@ f @@@ fct]; Select[Range[10^6], q] (* _Amiram Eldar_, Aug 06 2022 *)
%o A356420 (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
%o A356420 Psi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
%o A356420 isok(k) = if (k==1, return(1)); my(x); ispower(Psi(k),, &x) && (x == rad(k));
%Y A356420 Cf. A001615, A007947, A355045.
%K A356420 nonn
%O A356420 1,2
%A A356420 _Michel Marcus_, Aug 06 2022
%E A356420 More terms from _Jinyuan Wang_, Aug 06 2022