A072512 Product of all n - d, where 1 < d < n and d is a divisor of n.

1, 1, 1, 2, 1, 12, 1, 24, 6, 40, 1, 4320, 1, 84, 120, 1344, 1, 25920, 1, 43200, 252, 220, 1, 31933440, 20, 312, 432, 183456, 1, 136080000, 1, 322560, 660, 544, 840, 12563527680, 1, 684, 936, 919296000, 1, 1155772800, 1, 1219680, 1814400, 1012, 1

Offset: 1

Author

Amarnath Murthy, Jul 28 2002

Keywords

• nonn
• look

Comments

For prime p, a(p) = 1.

If n is not a prime or the square of a prime then n divides a(n).

Examples

			For n = 16 the nontrivial divisors d are 2,4 and 8, so a(16) = (16-2)*(16-4)*(16-8) = 14*12*8 = 1344.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072513.

Programs

Maple

f:= proc(n) local d; mul(n-d, d = numtheory:-divisors(n) minus {1,n}) end proc:
map(f, [$1..50]); # Robert Israel, Dec 30 2024

PARI

a(n) = my(d=divisors(n)); prod(j=2, matsize(d)[2]-1, n-d[j]);

Extensions

Edited and extended by Klaus Brockhaus, Jul 31 2002