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Number of partitions of n into two parts such that the positive difference of the parts is semiprime.
3

%I #8 Apr 16 2018 19:01:43

%S 0,0,0,0,0,1,0,2,0,2,1,3,1,3,1,4,2,4,2,4,2,4,3,5,3,5,4,6,4,6,4,6,4,6,

%T 5,7,6,7,6,8,7,8,7,8,7,8,7,9,7,9,8,9,9,9,9,9,10,9,11,10,11,10,11,11,

%U 11,11,12,11,12,11,13,11,13,11,13,12,13,12,14

%N Number of partitions of n into two parts such that the positive difference of the parts is semiprime.

%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(n-2i) == 2], where Omega = A001222 and [] is the Iverson bracket.

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

%o (PARI) a(n) = sum(i=1, (n-1)\2, bigomega(n-2*i)==2); \\ _Michel Marcus_, Apr 11 2018

%Y Cf. A001222, A302604, A302643.

%K nonn,easy

%O 1,8

%A _Wesley Ivan Hurt_, Apr 10 2018