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A261927 Sum of the larger parts of the partitions of n into two squarefree parts. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..58.

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}]

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

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Last modified January 23 20:47 EST 2022. Contains 350515 sequences. (Running on oeis4.)