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Sum of the smaller parts of the partitions of 2n into two parts with larger part squarefree.
1

%I #13 Sep 17 2020 17:08:11

%S 1,3,4,6,12,14,15,17,28,41,44,48,64,67,68,70,89,93,116,122,149,157,

%T 163,169,199,230,235,268,303,311,318,325,364,372,379,387,432,441,448,

%U 456,504,512,519,527,580,635,644,654,713,773,834,846,911,925,994,1010

%N Sum of the smaller parts of the partitions of 2n into two parts with larger part squarefree.

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

%F a(n) = Sum_{i=1..n} i * mu(2*n-i)^2, where mu is the Möbius function (A008683).

%t Table[Sum[i*MoebiusMu[2 n - i]^2, {i, n}], {n, 80}]

%Y Cf. A008683, A008966, A294143.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, Oct 23 2017