A280320 - OEIS

%I #25 Jan 22 2023 12:05:04

%S 1,5,10,14,34,66,59,75,84,220,205,309,373,600,565,665,839,1103,959,

%T 1191,1176,1860,1416,2060,1664,3653,2194,3505,2891,4974,3563,5534,

%U 4371,7551,5845,8874,6742,10409,7061,10145,8037,12414,9030,13327,10849,15319,13473,15960

%N Sum of the squares of the smaller parts of the partitions of 2n into two squarefree parts.

%H Harvey P. Dale, <a href="/A280320/b280320.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%F a(n) = A280316(n) - A280322(n).

%p with(numtheory): A280320:=n->add(i^2*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280320(n), n=1..100);

%t Table[Total[Select[IntegerPartitions[2 n,{2}],AllTrue[#,SquareFreeQ]&][[All,2]]^2],{n,50}] (* _Harvey P. Dale_, Jan 22 2023 *)

%o (PARI) a(n) = sum(i=1, n, i^2*issquarefree(i)*issquarefree(2*n-i)); \\ _Michel Marcus_, May 16 2019

%Y Cf. A008683, A280226, A280316, A280322.

%K nonn,easy

%O 1,2

%A _Wesley Ivan Hurt_, Dec 31 2016