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A326443 Number of partitions of n into 8 squarefree parts. 11
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 9, 13, 15, 21, 24, 32, 36, 47, 53, 68, 75, 94, 105, 130, 143, 174, 192, 231, 254, 301, 330, 389, 424, 495, 539, 626, 678, 781, 847, 970, 1048, 1192, 1287, 1461, 1572, 1772, 1908, 2144, 2301, 2573, 2762, 3079, 3295 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,11
LINKS
FORMULA
a(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) = A326444(n)/n for n > 0.
MATHEMATICA
Table[Count[IntegerPartitions[n, {8}], _?(AllTrue[#, SquareFreeQ]&)], {n, 0, 60}] (* Harvey P. Dale, Mar 10 2023 *)
CROSSREFS
Sequence in context: A360142 A308952 A302401 * A326522 A326626 A341153
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 06 2019
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)