A381885 a(n) = Product_{k=2..n-1} k^ord(n, k) where ord(n, k) = 0 if k does not divide n, otherwise is the exponent of the highest power of k that divides n.

1, 1, 1, 4, 1, 6, 1, 32, 9, 10, 1, 288, 1, 14, 15, 2048, 1, 972, 1, 800, 21, 22, 1, 55296, 25, 26, 243, 1568, 1, 27000, 1, 65536, 33, 34, 35, 10077696, 1, 38, 39, 256000, 1, 74088, 1, 3872, 6075, 46, 1, 169869312, 49, 12500, 51, 5408, 1, 1417176, 55, 702464, 57

Offset

1,4

Links

Table of n, a(n) for n=1..57.

Wikipedia, p-adic valuation.

Formula

If the base of the factors of the product is restricted to prime numbers then A005451 is generated.

a(p) = 1 if p is prime.

a(n) = A364813(n) / n.

Maple

with(padic): a := n -> local k; mul(k^ordp(n, k), k = 2.. n-1): seq(a(n), n = 1..57);

Mathematica

Table[Product[k^IntegerExponent[n, k], {k, 2, n - 1}], {n, 1, 57}]

Prog

(PARI) a(n) = prod(k=2, n-1, k^valuation(n, k)); \\ Michel Marcus, Apr 01 2025

Crossrefs

Cf. A364813, A005451.

Sequence in context: A344442 A316223 A087652 * A072195 A032310 A032220

Adjacent sequences: A381882 A381883 A381884 * A381886 A381887 A381888

Keyword

nonn

Author

Peter Luschny, Apr 01 2025

Status

approved