

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
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OFFSET

1,3


COMMENTS

Row products of triangle A193829, if n >= 2.  Omar E. Pol, Aug 31 2011
When p is prime a(p) = p1.  Michel Marcus, May 15 2014


LINKS

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


FORMULA

a(n) = product(A027750(n,k+1)A027750(n,k): k=1..A001221(n)1.  Reinhard Zumkeller, Jun 23 2013


EXAMPLE

Since positive divisors of 12 are 1, 2, 3, 4, 6 and 12, a(12) = (21) *(32) *(43) *(64) *(126) = 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, #d1, d[i+1]  d[i]); } \\ Michel Marcus, May 15 2014


CROSSREFS

Sequence in context: A293170 A101200 A122585 * A286931 A265701 A007439
Adjacent sequences: A057446 A057447 A057448 * A057450 A057451 A057452


KEYWORD

nonn,look


AUTHOR

Leroy Quet, Sep 25 2000


STATUS

approved



