%I #8 Apr 20 2020 01:09:08

%S 0,0,0,0,1,1,2,1,2,2,3,3,3,2,3,4,2,4,3,5,5,4,2,6,4,5,6,6,4,8,4,9,6,10,

%T 6,11,3,8,7,10,6,9,6,9,9,11,5,13,7,13,8,11,6,15,8,14,10,13,8,17,10,14,

%U 10,15,8,19,9,17,14,16,10,22,12,17,15,16,12

%N Number of ways to write n as the sum of two distinct positive integers with the same number of distinct prime factors.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{i=1..floor((n-1)/2)} [omega(i) = omega(n-i)], where [] is the Iverson bracket and omega is the number of distinct prime factors of n (A001221).

%t Table[Sum[KroneckerDelta[PrimeNu[i], PrimeNu[n - i]], {i, Floor[(n - 1)/2]}], {n, 100}]

%Y Cf. A001221 (omega), A333701.

%K nonn,easy

%O 1,7

%A _Wesley Ivan Hurt_, Apr 02 2020