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A326444 Sum of all the parts in the partitions of n into 8 squarefree parts. 9
0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 20, 22, 48, 65, 112, 135, 208, 255, 378, 456, 640, 756, 1034, 1219, 1632, 1875, 2444, 2835, 3640, 4147, 5220, 5952, 7392, 8382, 10234, 11550, 14004, 15688, 18810, 21021, 25040, 27798, 32802, 36421, 42680, 47160, 54832, 60489 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

FORMULA

a(n) = n * Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/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)^2, where mu is the Möbius function (A008683).

a(n) = n * A326443(n).

a(n) = A326445(n) + A326446(n) + A326447(n) + A326448(n) + A326449(n) + A326450(n) + A326451(n) + A326452(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[n * MoebiusMu[p]^2 * MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^2 * MoebiusMu[n - i - j - k - l - m - o - p]^2, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]

CROSSREFS

Cf. A008683, A326443, A326445, A326446, A326447, A326448, A326449, A326450, A326451, A326452.

Sequence in context: A240915 A281225 A071869 * A309484 A308989 A048124

Adjacent sequences: A326441 A326442 A326443 * A326445 A326446 A326447

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 06 2019

STATUS

approved

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Last modified December 9 17:01 EST 2022. Contains 358701 sequences. (Running on oeis4.)