A262042 First column of A261987.
4, 8, 25, 91, 115, 527, 527, 1331, 1331, 4301, 15689, 14111, 19337, 31427, 175151, 175151, 175151, 175151, 175151
Offset: 1
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(4) = 5. There are two partitions of 4 into two squarefree parts: (3, 1) and (2, 2). The sum of the larger parts of these partitions is 3 + 2 = 5. a(5) = 3. There is only one partition of 5 into two squarefree parts: (3, 2). The larger part is 3, thus a(5) = 3.
with(numtheory): A261987:=n->add((n-i)*mobius(i)^2*mobius(n-i)^2, i=1..floor(n/2)): seq(A261987(n), n=1..70);
Table[Sum[(n - i) MoebiusMu[i]^2 * MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 70}]
Table[Total[Select[IntegerPartitions[n,{2}],AllTrue[#,SquareFreeQ]&][[All,1]]],{n,60}] (* Harvey P. Dale, Apr 26 2022 *)
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