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a(n) = n^npf(n) / rad(n), where npf(n) is the number of prime factors with multiplicity of n.
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%I #21 Jul 12 2023 10:08:43

%S 1,1,1,8,1,6,1,256,27,10,1,288,1,14,15,32768,1,972,1,800,21,22,1,

%T 55296,125,26,6561,1568,1,900,1,16777216,33,34,35,279936,1,38,39,

%U 256000,1,1764,1,3872,6075,46,1,42467328,343,12500,51,5408,1,1417176,55,702464

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

%H Michael De Vlieger, <a href="/A363923/b363923.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n^A001222(n) / A007947(n).

%F a(n) = 1 <=> n term of A008578.

%p with(NumberTheory): a := n -> n^NumberOfPrimeFactors(n) / Radical(n):

%p seq(a(n), n = 1..56);

%t Array[#^PrimeOmega[#]/(Times @@ FactorInteger[#][[All, 1]]) &, 56] (* _Michael De Vlieger_, Jul 11 2023 *)

%o (PARI) a(n) = my(f=factor(n)); n^bigomega(f)/factorback(f[, 1]); \\ _Michel Marcus_, Jul 11 2023

%o (Python)

%o from math import prod

%o from sympy import factorint

%o def A363923(n): return prod(n**e//p for p, e in factorint(n).items()) # _Chai Wah Wu_, Jul 12 2023

%Y Cf. A001222, A007947, A205959, A008578.

%K nonn

%O 1,4

%A _Peter Luschny_, Jul 11 2023