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

1, 1, 2, 6, 12, 60, 360, 2520, 5040, 15120, 151200, 1663200, 19958400, 259459200, 3632428800, 54486432000, 108972864000, 1852538688000, 33345696384000, 633568231296000, 12671364625920000, 266098657144320000, 5854170457175040000, 134645920515025920000

Offset: 0

Author

Amarnath Murthy, Feb 26 2002

Keywords

• easy
• nonn

Comments

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

Examples

			a(8) = 1*2*3*2*5*6*7*2 = 5040.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..462 (first 37 terms from Hal M. Switkay)

Crossrefs

Partial products of A052410.

Cf. A000142, A048803.

Programs

Maple

b:= proc(n) option remember; (l-> (t-> mul(i[1]^(i[2]/t),
       i=l))(igcd(seq(i[2], i=l))))(ifactors(n)[2])
    end:
a:= proc(n) option remember; `if`(n<1, 1, a(n-1)*b(n)) end:
seq(a(n), n=0..23);  # Alois P. Heinz, Jul 22 2024

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 22 2024