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 A309478 Sum of the squarefree parts of the partitions of n into 3 parts. 8
 0, 0, 0, 3, 4, 10, 14, 24, 32, 51, 56, 77, 95, 128, 146, 198, 225, 280, 318, 384, 416, 524, 549, 672, 726, 861, 915, 1063, 1143, 1292, 1382, 1551, 1661, 1867, 1966, 2211, 2355, 2618, 2762, 3094, 3263, 3602, 3798, 4185, 4409, 4869, 5078, 5524, 5794, 6264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS David A. Corneth, Table of n, a(n) for n = 0..9999 Index entries for sequences related to partitions FORMULA a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (i * mu(i)^2 + j * mu(j)^2 + (n-i-j) * mu(n-i-j)^2), where mu is the Möbius function (A008683). EXAMPLE Figure 1: The partitions of n into 3 parts for n = 3, 4, ... 1+1+8 1+1+7 1+2+7 1+2+6 1+3+6 1+1+6 1+3+5 1+4+5 1+1+5 1+2+5 1+4+4 2+2+6 1+1+4 1+2+4 1+3+4 2+2+5 2+3+5 1+1+3 1+2+3 1+3+3 2+2+4 2+3+4 2+4+4 1+1+1 1+1+2 1+2+2 2+2+2 2+2+3 2+3+3 3+3+3 3+3+4 ... ----------------------------------------------------------------------- n | 3 4 5 6 7 8 9 10 ... ----------------------------------------------------------------------- a(n) | 3 4 10 14 24 32 51 56 ... ----------------------------------------------------------------------- MATHEMATICA Table[Sum[Sum[i*MoebiusMu[i]^2 + j*MoebiusMu[j]^2 + (n - i - j) MoebiusMu[n - i - j]^2, {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 50}] Table[Total[Select[Flatten[IntegerPartitions[n, {3}]], SquareFreeQ]], {n, 0, 50}] (* Harvey P. Dale, Apr 09 2022 *) CROSSREFS Cf. A008683, A309455, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486. Sequence in context: A035594 A167273 A096380 * A329805 A071019 A173285 Adjacent sequences: A309475 A309476 A309477 * A309479 A309480 A309481 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Aug 04 2019 STATUS approved

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Last modified June 9 23:59 EDT 2023. Contains 363183 sequences. (Running on oeis4.)