A387151 a(n) = n*n! / Product_{k=1..n} radical(k), where radical(n) is the product of distinct prime factors of n, cf. A007947.

0, 1, 2, 3, 8, 10, 12, 14, 64, 216, 240, 264, 576, 624, 672, 720, 6144, 6528, 20736, 21888, 46080, 48384, 50688, 52992, 221184, 1152000, 1198080, 11197440, 23224320, 24053760, 24883200, 25712640, 424673280, 437944320, 451215360, 464486400, 2866544640

Offset: 0

Author

David A. Corneth and Peter Luschny, Aug 18 2025

Keywords

• nonn
• new

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..3167

Crossrefs

Cf. A387140.

Programs

Maple

A387151 := n -> n*n! / mul(NumberTheory:-Radical(k), k = 1..n): seq(A387151(n), n = 0..36);

Mathematica

k = 1; {0}~Join~Reap[Do[k *= Times @@ FactorInteger[n][[;; , 1]]; Sow[n*n!/k], {n, 36}] ][[-1, 1]] (* Michael De Vlieger, Aug 18 2025 *)

Formula

a(n) = n! / A387140(n) for n >= 1.