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A356420
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Integers k such that for some m >= 0, psi(k) = rad(k)^m, where psi(k) = A001615(k) and rad(k) = A007947(k).
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0
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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