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

1, 18, 108, 648, 3888, 11250, 23328, 139968, 337500, 501126, 839808, 5038848, 8696754, 10125000, 30233088, 51114852, 57177414, 181398528, 303750000, 573985764, 1088391168, 2401451388, 5018345916, 5213714904, 6530347008, 9112500000, 23981814018, 26622318750, 37883060424

Offset: 1

Author

Michel Marcus, Aug 06 2022

Keywords

• nonn

Comments

Inspired by A355045, which has an additional constraint.

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

Crossrefs

Cf. A001615, A007947, A355045.

Programs

Mathematica

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 *)

PARI

rad(n) = factorback(factorint(n)[, 1]); \\ A007947
Psi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
isok(k) = if (k==1, return(1)); my(x); ispower(Psi(k),, &x) && (x == rad(k));

Extensions

More terms from Jinyuan Wang, Aug 06 2022