A136529 a(n) = the smallest possible number of positive divisors of the sum of any two distinct positive divisors of n.

2, 3, 2, 4, 2, 4, 2, 3, 2, 6, 2, 4, 2, 3, 2, 6, 2, 6, 2, 3, 2, 8, 2, 4, 2, 3, 2, 8, 2, 6, 2, 3, 2, 4, 2, 4, 2, 3, 2, 8, 2, 6, 2, 3, 2, 10, 2, 4, 2, 3, 2, 8, 2, 4, 2, 3, 2, 12, 2, 4, 2, 3, 2, 4, 2, 6, 2, 3, 2, 12, 2, 4, 2, 3, 2, 4, 2, 10, 2, 3, 2, 12, 2, 4, 2, 3, 2, 12, 2, 4, 2, 3, 2, 4, 2, 6, 2, 3, 2, 8, 2, 8

Offset

2,1

Comments

There are d(n)*(d(n)-1)/2 sums of pairs of distinct positive divisors of n, where d(n) = number of positive divisors of n.

Links

Antti Karttunen, Table of n, a(n) for n = 2..65537

Example

The positive divisors of 6 are 1,2,3,6. Letting d(m) = the number of positive divisors of m: d(1+2)=2; d(1+3)=3; d(1+6)=2; d(2+3)=2; d(2+6)=4; d(3+6)=3. The least of these values is 2, so a(6) = 2.

Prog

(PARI) { a(n) = d=divisors(n); m=numdiv(n+1); for(i=1, #d, for(j=i+1, #d, m=min(m, numdiv(d[i]+d[j])); )); m } \\ Max Alekseyev, Apr 27 2009

Crossrefs

Cf. A136528.

Sequence in context: A286602 A286600 A339013 * A113982 A256542 A101743

Adjacent sequences: A136526 A136527 A136528 * A136530 A136531 A136532

Keyword

nonn

Author

Leroy Quet, Jan 03 2008

Extensions

Extended by Max Alekseyev, Apr 27 2009

Status

approved