A057449 Product of differences between consecutive positive divisors of n.

1, 1, 2, 2, 4, 3, 6, 8, 12, 15, 10, 12, 12, 35, 40, 64, 16, 81, 18, 100, 112, 99, 22, 192, 80, 143, 216, 588, 28, 600, 30, 1024, 352, 255, 224, 1944, 36, 323, 520, 2400, 40, 3087, 42, 3388, 2880, 483, 46, 12288, 252, 5625, 952, 6084, 52, 19683, 1056, 14112, 1216

Offset: 1

Author

Leroy Quet, Sep 25 2000

Keywords

• nonn
• look

Comments

Row products of triangle A193829, if n >= 2. - Omar E. Pol, Aug 31 2011

When p is prime a(p) = p-1. - Michel Marcus, May 15 2014

Examples

			Since positive divisors of 12 are 1, 2, 3, 4, 6 and 12, a(12) = (2-1) *(3-2) *(4-3) *(6-4) *(12-6) = 1 *1 *1 *2 *6 = 12.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Programs

Haskell

a057449 = product . a193829_row  -- Reinhard Zumkeller, Jun 23 2013

Mathematica

Times@@Differences[Divisors[#]]&/@Range[80]  (* Harvey P. Dale, Apr 20 2011 *)

PARI

a(n) = {my(d = divisors(n)); prod(i=1, #d-1, d[i+1] - d[i]);} \\ Michel Marcus, May 15 2014

Formula

a(n) = Product_{k=1..A000005(n)-1} A027750(n,k+1)-A027750(n,k). - Reinhard Zumkeller, Jun 23 2013