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URL: https://oeis.org/A363918

⇱ A363918 - OEIS

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A363918
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.
1
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, 2187, 56, 1, 1, 1, 5242880, 1, 1, 1, 5184, 1, 1, 1, 4800, 1, 1, 1, 88, 90, 1, 1, 442368, 98, 100, 1, 104, 1, 8748, 1, 9408, 1, 1, 1, 120, 1, 1, 126, 6442450944, 1, 1, 1, 136
OFFSET
1,4
FORMULA
a(n) / A363919(n) = A005361(n).
a(n) * A205959(n) = A005361(n) * A363923(n) = A363917(n).
MAPLE
a := n -> local p: mul(p[2] * n^(p[2] - 1), p in ifactors(n)[2]):
seq(a(n), n = 1..68);
PROG
(PARI) a(n) = my(f=factor(n)[, 2]); vecprod(f)*n^(vecsum(f)-#f); \\ Michel Marcus, Jul 19 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 19 2023
STATUS
approved