A261927 Sum of the larger parts of the partitions of n into two squarefree parts.

0, 1, 2, 5, 3, 8, 11, 18, 13, 12, 16, 34, 28, 31, 37, 63, 50, 56, 44, 88, 59, 83, 73, 129, 93, 91, 100, 138, 105, 103, 123, 195, 151, 173, 169, 303, 201, 199, 219, 345, 255, 256, 298, 442, 341, 274, 289, 482, 380, 294, 255, 525, 401, 410, 270, 539, 422, 487

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for sequences related to partitions

Formula

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

a(n) = A262351(n) - A261985(n).

Example

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.

Maple

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);

Mathematica

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 *)

Crossrefs

Cf. A008683, A071068, A261985, A262351.

Sequence in context: A292965 A302054 A081146 * A262870 A294210 A244418

Adjacent sequences: A261924 A261925 A261926 * A261928 A261929 A261930

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 02 2015

Status

approved