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A363923 a(n) = n^npf(n) / rad(n), where npf(n) is the number of prime factors with multiplicity of n.

%I A363923 #21 Jul 12 2023 10:08:43
%S A363923 1,1,1,8,1,6,1,256,27,10,1,288,1,14,15,32768,1,972,1,800,21,22,1,
%T A363923 55296,125,26,6561,1568,1,900,1,16777216,33,34,35,279936,1,38,39,
%U A363923 256000,1,1764,1,3872,6075,46,1,42467328,343,12500,51,5408,1,1417176,55,702464
%N A363923 a(n) = n^npf(n) / rad(n), where npf(n) is the number of prime factors with multiplicity of n.
%H A363923 Michael De Vlieger, <a href="/A363923/b363923.txt">Table of n, a(n) for n = 1..10000</a>
%F A363923 a(n) = n^A001222(n) / A007947(n).
%F A363923 a(n) = 1 <=> n term of A008578.
%p A363923 with(NumberTheory): a := n -> n^NumberOfPrimeFactors(n) / Radical(n):
%p A363923 seq(a(n), n = 1..56);
%t A363923 Array[#^PrimeOmega[#]/(Times @@ FactorInteger[#][[All, 1]]) &, 56] (* _Michael De Vlieger_, Jul 11 2023 *)
%o A363923 (PARI) a(n) = my(f=factor(n)); n^bigomega(f)/factorback(f[, 1]); \\ _Michel Marcus_, Jul 11 2023
%o A363923 (Python)
%o A363923 from math import prod
%o A363923 from sympy import factorint
%o A363923 def A363923(n): return prod(n**e//p for p, e in factorint(n).items()) # _Chai Wah Wu_, Jul 12 2023
%Y A363923 Cf. A001222, A007947, A205959, A008578.
%K A363923 nonn
%O A363923 1,4
%A A363923 _Peter Luschny_, Jul 11 2023