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, 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

Links

Table of n, a(n) for n=1..68.

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

Cf. A363919, A363923, A005361, A205959, A303915, A363917.

Sequence in context: A181064 A010153 A360970 * A133421 A128881 A154015

Adjacent sequences: A363915 A363916 A363917 * A363919 A363920 A363921

Keyword

nonn

Author

Peter Luschny, Jul 19 2023

Status

approved