A309481 Sum of the squarefree parts of the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 6, 7, 16, 23, 46, 69, 116, 150, 227, 309, 442, 565, 787, 998, 1326, 1665, 2153, 2655, 3386, 4103, 5122, 6184, 7563, 8995, 10888, 12853, 15323, 17931, 21167, 24584, 28796, 33153, 38484, 44133, 50813, 57870, 66293, 75125, 85487, 96437, 109177

Offset

0,7

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Index entries for sequences related to partitions

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)} (i * mu(i)^2 + j * mu(j)^2 + k * mu(k)^2 + l * mu(l)^2 + m * mu(m)^2 + (n-i-j-k-l-m) * mu(n-i-j-k-l-m)^2), where mu is the Möbius function (A008683).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[i * MoebiusMu[i]^2 + j * MoebiusMu[j]^2 + k * MoebiusMu[k]^2 + l * MoebiusMu[l]^2 + m * MoebiusMu[m]^2 + (n - i - j - k - l - m) * 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}]

Crossrefs

Cf. A008683, A309458, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.

Sequence in context: A308903 A315845 A322638 * A308867 A315846 A062850

Adjacent sequences: A309478 A309479 A309480 * A309482 A309483 A309484

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 04 2019

Status

approved