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A068625 Reduced root factorial of n: product of the smallest integer root of numbers from 1 to n.

%I A068625 #31 Jul 23 2024 08:18:37
%S A068625 1,1,2,6,12,60,360,2520,5040,15120,151200,1663200,19958400,259459200,
%T A068625 3632428800,54486432000,108972864000,1852538688000,33345696384000,
%U A068625 633568231296000,12671364625920000,266098657144320000,5854170457175040000,134645920515025920000
%N A068625 Reduced root factorial of n: product of the smallest integer root of numbers from 1 to n.
%C A068625 A "binomial" style a(m+n)/(a(m)*a(n)) is not always an integer, as for instance at m = n = 18 (unlike ordinary factorials or A048803). - _Hal M. Switkay_, Jul 22 2024
%H A068625 Alois P. Heinz, <a href="/A068625/b068625.txt">Table of n, a(n) for n = 0..462</a> (first 37 terms from Hal M. Switkay)
%e A068625 a(8) = 1*2*3*2*5*6*7*2 = 5040.
%p A068625 b:= proc(n) option remember; (l-> (t-> mul(i[1]^(i[2]/t),
%p A068625        i=l))(igcd(seq(i[2], i=l))))(ifactors(n)[2])
%p A068625     end:
%p A068625 a:= proc(n) option remember; `if`(n<1, 1, a(n-1)*b(n)) end:
%p A068625 seq(a(n), n=0..23);  # _Alois P. Heinz_, Jul 22 2024
%Y A068625 Partial products of A052410.
%Y A068625 Cf. A000142, A048803.
%K A068625 easy,nonn
%O A068625 0,3
%A A068625 _Amarnath Murthy_, Feb 26 2002
%E A068625 a(0)=1 prepended by _Alois P. Heinz_, Jul 22 2024