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A308902
Number of partitions of n into 6 squarefree parts.
10
0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 8, 11, 13, 18, 19, 25, 27, 36, 39, 48, 52, 66, 70, 85, 91, 111, 117, 139, 148, 176, 185, 214, 227, 266, 278, 318, 336, 387, 405, 459, 482, 550, 574, 644, 676, 764, 796, 885, 929, 1038, 1082, 1194, 1247, 1385, 1440, 1580
OFFSET
0,9
FORMULA
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-k-j-l-m)^2, where mu is the Möbius function (A008683).
a(n) = A308903(n)/n.
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[MoebiusMu[i]^2*MoebiusMu[j]^2*MoebiusMu[k]^2* MoebiusMu[l]^2*MoebiusMu[m]^2*MoebiusMu[n - i - j - k - l - m]^2, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 29 2019
STATUS
approved