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%I #9 Jul 19 2023 07:48:16
%S 1,1,1,8,1,1,1,192,18,1,1,24,1,1,1,16384,1,36,1,40,1,1,1,1728,50,1,
%T 2187,56,1,1,1,5242880,1,1,1,5184,1,1,1,4800,1,1,1,88,90,1,1,442368,
%U 98,100,1,104,1,8748,1,9408,1,1,1,120,1,1,126,6442450944,1,1,1,136
%N a(n) = Product_{p in Factors(n)} mult(p)*n^(mult(p) - 1), where Factors(n) is the integer factorization of n and mult(p) the multiplicity of the prime factor p.
%F a(n) / A363919(n) = A005361(n).
%F a(n) * A205959(n) = A005361(n) * A363923(n) = A363917(n).
%p a := n -> local p: mul(p[2] * n^(p[2] - 1), p in ifactors(n)[2]):
%p seq(a(n), n = 1..68);
%o (PARI) a(n) = my(f=factor(n)[, 2]); vecprod(f)*n^(vecsum(f)-#f); \\ _Michel Marcus_, Jul 19 2023
%Y Cf. A363919, A363923, A005361, A205959, A303915, A363917.
%K nonn
%O 1,4
%A _Peter Luschny_, Jul 19 2023
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