|
%I #29 May 16 2014 03:35:13
%S 1,1,2,2,4,3,6,8,12,15,10,12,12,35,40,64,16,81,18,100,112,99,22,192,
%T 80,143,216,588,28,600,30,1024,352,255,224,1944,36,323,520,2400,40,
%U 3087,42,3388,2880,483,46,12288,252,5625,952,6084,52,19683,1056,14112,1216
%N Product of differences between consecutive positive divisors of n.
%C Row products of triangle A193829, if n >= 2. - _Omar E. Pol_, Aug 31 2011
%C When p is prime a(p) = p-1. - _Michel Marcus_, May 15 2014
%H Alois P. Heinz, <a href="/A057449/b057449.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = product(A027750(n,k+1)-A027750(n,k): k=1..A001221(n)-1. - _Reinhard Zumkeller_, Jun 23 2013
%e 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.
%t Times@@Differences[Divisors[#]]&/@Range[80] (* _Harvey P. Dale_, Apr 20 2011 *)
%o (Haskell)
%o a057449 = product . a193829_row -- _Reinhard Zumkeller_, Jun 23 2013
%o (PARI) a(n) = {my(d = divisors(n)); prod(i=1, #d-1, d[i+1] - d[i]);} \\ _Michel Marcus_, May 15 2014
%K nonn,look
%O 1,3
%A _Leroy Quet_, Sep 25 2000
|
