A069625 Number of distinct numbers that can be formed as a product of two or more divisors of n.

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, 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, 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

Offset

1,4

Comments

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.

The positions of records are: 1, 2, 4, 6, 12, 24, 30, 36, 48, 60, 120, 180, 210, 240, ... - Antti Karttunen, May 19 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..359

Formula

a(n) = A207329(n) - 1. - Michel Marcus, Sep 17 2013

Example

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.

Prog

(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

Crossrefs

Sequence in context: A239303 A040011 A066446 * A111614 A193279 A076889

Adjacent sequences: A069622 A069623 A069624 * A069626 A069627 A069628

Keyword

nonn

Author

Amarnath Murthy, Mar 27 2002

Extensions

Corrected and extended by David Wasserman, Apr 23 2003

Status

approved