%I #13 May 20 2017 07:12:55
%S 0,1,1,3,1,6,1,6,3,6,1,19,1,6,6,10,1,19,1,19,6,6,1,44,3,6,6,19,1,58,1,
%T 15,6,6,6,65,1,6,6,44,1,58,1,19,19,6,1,85,3,19,6,19,1,44,6,44,6,6,1,
%U 268,1,6,19,21,6,58,1,19,6,58,1,156,1,6,19,19,6,58,1,85,10,6,1,268,6,6,6,44
%N Number of distinct numbers that can be formed as a product of two or more divisors of n.
%C a(p) = 1, a(p*q) = 6, a(p^2*q) = 19, a(p^4)= 10 etc. where p and q are primes. Question: To find an expression for a(N) where N = p^a*q^b*r^c...p,q,r are primes.
%C The positions of records are: 1, 2, 4, 6, 12, 24, 30, 36, 48, 60, 120, 180, 210, 240, ... - _Antti Karttunen_, May 19 2017
%H Antti Karttunen, <a href="/A069625/b069625.txt">Table of n, a(n) for n = 1..359</a>
%F a(n) = A207329(n) - 1. - _Michel Marcus_, Sep 17 2013
%e a(6) = 6 as the divisors of 6 are 1, 2, 3 and 6 and the distinct products of these divisors are 2, 3, 6, 12, 18 and 36.
%o (PARI) a(n) = {d = divisors(n); s = Set(); for (i = 1, 2^#d, b = binary(i); if (sum(j = 1, #b, b[j]) > 1, s = Set(concat(s, prod(j = 1, #b, if (b[j] == 1, d[j], 1)))););); #s;} \\ _Michel Marcus_, Sep 17 2013
%K nonn
%O 1,4
%A _Amarnath Murthy_, Mar 27 2002
%E Corrected and extended by _David Wasserman_, Apr 23 2003