

A069625


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


2



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
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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



