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 A280251 Sum of the larger parts of the partitions of 2n into two squarefree parts. 4
 1, 5, 8, 18, 12, 34, 31, 63, 56, 88, 83, 129, 91, 138, 103, 195, 173, 303, 199, 345, 256, 442, 274, 482, 294, 525, 410, 539, 487, 668, 517, 714, 539, 913, 675, 1150, 776, 1131, 755, 1223, 783, 1406, 898, 1551, 1163, 1605, 1191, 1774, 1271, 1875, 1378, 2031, 1521, 2547 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..54. Index entries for sequences related to partitions FORMULA a(n) = Sum_{i=1..n} (2*n-i) * mu(i)^2 * mu(2*n-i)^2, where mu is the Möbius function (A008683). a(n) = A280252(n) - A280250(n). MAPLE with(numtheory): A280251:=n->sum((2*n-i)*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280251(n), n=1..100); MATHEMATICA Table[Total[Select[IntegerPartitions[2 n, {2}], AllTrue[#, SquareFreeQ]&][[;; , 1]]], {n, 60}] (* Harvey P. Dale, Apr 22 2023 *) CROSSREFS Cf. A008683, A187129, A280226, A280250, A280252. Sequence in context: A057592 A246638 A192170 * A104321 A196934 A359949 Adjacent sequences: A280248 A280249 A280250 * A280252 A280253 A280254 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Dec 29 2016 STATUS approved

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Last modified April 15 12:14 EDT 2024. Contains 371681 sequences. (Running on oeis4.)