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A294096 Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime and smaller part squarefree. 1

%I

%S 0,0,1,2,1,4,3,8,5,4,0,12,10,20,11,16,5,28,22,38,18,28,14,48,34,32,7,

%T 24,26,56,30,64,47,68,23,60,34,68,54,58,21,112,85,144,59,104,62,168,

%U 82,124,61,110,83,180,81,124,71,152,62,202,91,192,132,224,74

%N Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime and smaller part squarefree.

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

%F a(n) = Sum_{i=1..floor(n/2)} (n - 2i) * A008966(i) * A010051(n - i).

%t Table[Sum[(n - 2 i) (PrimePi[n - i] - PrimePi[n - i - 1]) MoebiusMu[i]^2, {i, Floor[n/2]}], {n, 80}]

%Y Cf. A010051, A008966, A294095.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Oct 22 2017

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Last modified October 16 05:41 EDT 2021. Contains 348035 sequences. (Running on oeis4.)