A136528 a(n) = the highest possible number of positive divisors of the sum of any two distinct positive divisors of n.

2, 3, 4, 4, 4, 4, 6, 6, 6, 6, 6, 4, 5, 6, 8, 6, 8, 6, 8, 8, 8, 8, 9, 8, 6, 9, 8, 8, 9, 6, 10, 9, 9, 9, 10, 4, 8, 8, 12, 8, 10, 6, 10, 12, 10, 10, 12, 8, 12, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 4, 7, 12, 12, 8, 12, 6, 12, 12, 12, 12, 12, 4, 6, 12, 10, 12, 12, 10, 16, 12, 12, 12, 12, 12, 8, 12, 12, 12, 16, 8, 12, 12, 12, 12, 16

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

Table of n, a(n) for n=2..96.

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 maximum of these values is 4, so a(6) = 4.

Crossrefs

Cf. A136529.

Sequence in context: A195849 A372450 A087827 * A263252 A276334 A225486

Adjacent sequences: A136525 A136526 A136527 * A136529 A136530 A136531

Keyword

nonn

Author

Leroy Quet, Jan 03 2008

Extensions

More terms from Sean A. Irvine, Feb 28 2011

Status

approved