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 A326527 Sum of the sixth largest parts of the partitions of n into 9 squarefree parts. 10
 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 9, 11, 16, 21, 29, 35, 49, 57, 77, 91, 118, 137, 177, 202, 255, 293, 363, 413, 509, 580, 707, 802, 969, 1097, 1319, 1481, 1764, 1980, 2337, 2615, 3069, 3421, 3982, 4431, 5126, 5689, 6553, 7240, 8301, 9169, 10451 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Table of n, a(n) for n=0..55. Index entries for sequences related to partitions FORMULA a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} mu(q)^2 * mu(p)^2 * mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o-p-q)^2 * m, where mu is the Möbius function (A008683). a(n) = A326523(n) - A326524(n) - A326525(n) - A326526(n) - A326528(n) - A326529(n) - A326530(n) - A326531(n) - A326532(n). MATHEMATICA Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, SquareFreeQ]&][[All, 6]]], {n, 0, 60}] (* Harvey P. Dale, Jul 05 2022 *) CROSSREFS Cf. A008683, A326522, A326523, A326524, A326525, A326526, A326528, A326529, A326530, A326531, A326532. Sequence in context: A308955 A098386 A326447 * A326632 A240206 A229816 Adjacent sequences: A326524 A326525 A326526 * A326528 A326529 A326530 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jul 11 2019 STATUS approved

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Last modified March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)