A294245 - OEIS

%I #16 Sep 17 2020 17:02:59

%S 0,0,4,4,17,17,29,29,37,46,66,66,103,130,158,158,174,174,192,192,212,

%T 212,301,301,374,399,451,478,506,506,566,629,661,661,729,729,765,840,

%U 916,916,1037,1037,1121,1121,1165,1210,1302,1302,1350,1498,1548,1548

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

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

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

%t Table[Sum[(2 n - k) (1 - MoebiusMu[2 n - k]^2), {k, n}], {n, 80}]

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

%Y Cf. A008683, A008966, A294246.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Oct 25 2017