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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.

%I A387151 #10 Aug 18 2025 18:50:37
%S A387151 0,1,2,3,8,10,12,14,64,216,240,264,576,624,672,720,6144,6528,20736,
%T A387151 21888,46080,48384,50688,52992,221184,1152000,1198080,11197440,
%U A387151 23224320,24053760,24883200,25712640,424673280,437944320,451215360,464486400,2866544640
%N 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.
%H A387151 Michael De Vlieger, <a href="/A387151/b387151.txt">Table of n, a(n) for n = 0..3167</a>
%F A387151 a(n) = n! / A387140(n) for n >= 1.
%p A387151 A387151 := n -> n*n! / mul(NumberTheory:-Radical(k), k = 1..n): seq(A387151(n), n = 0..36);
%t A387151 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 *)
%Y A387151 Cf. A387140.
%K A387151 nonn,new
%O A387151 0,3
%A A387151 _David A. Corneth_ and _Peter Luschny_, Aug 18 2025