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A326523 Sum of all the parts in the partitions of n into 9 squarefree parts. 10
0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 22, 24, 52, 70, 120, 144, 221, 288, 418, 500, 714, 858, 1173, 1392, 1850, 2184, 2862, 3304, 4263, 4950, 6231, 7136, 8910, 10234, 12530, 14256, 17316, 19684, 23673, 26640, 31816, 35826, 42355, 47388, 55755, 62284, 72662 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
LINKS
FORMULA
a(n) = 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, where mu is the Möbius function (A008683).
a(n) = n * A326522(n).
a(n) = A326524(n) + A326525(n) + A326526(n) + A326527(n) + A326528(n) + A326529(n) + A326530(n) + A326531(n) + A326532(n).
MATHEMATICA
Table[n*Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[MoebiusMu[q]^2 * 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 - q]^2, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 80}]
CROSSREFS
Sequence in context: A214425 A260184 A109463 * A061410 A309485 A228378
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 11 2019
STATUS
approved

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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)