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A057449
Product of differences between consecutive positive divisors of n.
2
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
1,3
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
LINKS
FORMULA
a(n) = Product_{k=1..A000005(n)-1} A027750(n,k+1)-A027750(n,k). - Reinhard Zumkeller, Jun 23 2013
EXAMPLE
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.
MATHEMATICA
Times@@Differences[Divisors[#]]&/@Range[80] (* Harvey P. Dale, Apr 20 2011 *)
PROG
(Haskell)
a057449 = product . a193829_row -- Reinhard Zumkeller, Jun 23 2013
(PARI) a(n) = {my(d = divisors(n)); prod(i=1, #d-1, d[i+1] - d[i]); } \\ Michel Marcus, May 15 2014
CROSSREFS
Sequence in context: A341469 A101200 A122585 * A308601 A286931 A374405
KEYWORD
nonn,look
AUTHOR
Leroy Quet, Sep 25 2000
STATUS
approved