cp's OEIS Frontend

A387140 a(n) = (1/n) * Product_{k=1..n} radical(k) for n >= 1, a(0) = 1, where radical(n) is the product of distinct prime factors of n, cf. A007947.

%I A387140 #10 Aug 18 2025 18:50:15
%S A387140 1,1,1,2,3,12,60,360,630,1680,15120,151200,831600,9979200,129729600,
%T A387140 1816214400,3405402000,54486432000,308756448000,5557616064000,
%U A387140 52797352608000,1055947052160000,22174888095360000,487847538097920000,2805123344063040000,13464592051502592000
%N A387140 a(n) = (1/n) * Product_{k=1..n} radical(k) for n >= 1, a(0) = 1, where radical(n) is the product of distinct prime factors of n, cf. A007947.
%F A387140 a(n) = A048803(n) / n for n >= 1.
%p A387140 a := n -> if n = 0 then 1 else mul(NumberTheory:-Radical(i), i=1..n) / n fi:
%t A387140 A387140[n_] := If[n == 0, 1, Quotient[Times @@ ResourceFunction["IntegerRadical"][Range[1, n]], n]]; Table[A387140[n], {n, 0, 25}]
%Y A387140 Cf. A007947, A048803, A387141.
%K A387140 nonn
%O A387140 0,4
%A A387140 _Peter Luschny_, Aug 18 2025