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%I #13 Apr 20 2020 01:05:34
%S 0,1,0,1,1,2,2,2,2,3,3,4,3,3,3,5,2,5,3,6,5,5,2,7,4,6,6,7,4,9,4,10,6,
%T 11,6,12,3,9,7,11,6,10,6,10,9,12,5,14,7,14,8,12,6,16,8,15,10,14,8,18,
%U 10,15,10,16,8,20,9,18,14,17,10,23,12,18,15,17
%N Number of ways to write n as the sum of two 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/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/2]}], {n, 100}]
%Y Cf. A001221, A333708 (distinct numbers).
%K nonn,easy
%O 1,6
%A _Wesley Ivan Hurt_, Apr 02 2020
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