A337531 - OEIS

%I #5 Sep 08 2020 22:00:48

%S 0,1,1,1,1,2,1,1,1,2,1,2,1,2,3,1,1,2,1,2,2,2,1,2,1,2,1,2,1,4,1,1,2,2,

%T 3,2,1,2,2,2,1,3,1,2,3,2,1,2,1,2,2,2,1,2,2,2,2,2,1,5,1,2,3,1,2,3,1,2,

%U 2,4,1,2,1,2,3,2,2,3,1,2,1,2,1,3,2,2,2,2,1,4,2,2,2,2,2,2

%N Number of ways that the divisors of 2n can be written as unordered sums of two other prime divisors of 2n (not necessarily distinct).

%F a(n) = Sum_{d1|(2*n), d2|(2*n), d3|(2*n), d1,d2 prime} [d1 + d2 = d3], where [ ] is the Iverson bracket.

%e a(15) = 3; The divisors of 2*15 = 30 are {1,2,3,5,6,10,15,30} and since 2 + 3 = 5, 3 + 3 = 6 and 5 + 5 = 10, a(15) = 3.

%Y Cf. A175393.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Aug 30 2020