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

1,4

Comments

For prime p, a(p) = 1.

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

Links

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

Example

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.

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

Prog

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

Crossrefs

Cf. A072513.

Sequence in context: A163088 A105608 A051190 * A271531 A118588 A259633

Adjacent sequences: A072509 A072510 A072511 * A072513 A072514 A072515

Keyword

nonn,look

Author

Amarnath Murthy, Jul 28 2002

Extensions

Edited and extended by Klaus Brockhaus, Jul 31 2002

Status

approved