A136528 - OEIS

%I #8 Apr 09 2014 10:12:26

%S 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,

%T 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,

%U 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

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

%C 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.

%e 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.

%Y Cf. A136529.

%K nonn

%O 2,1

%A _Leroy Quet_, Jan 03 2008

%E More terms from _Sean A. Irvine_, Feb 28 2011