A309482 Sum of the squarefree parts of the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 7, 8, 18, 26, 51, 76, 127, 178, 262, 363, 524, 687, 962, 1249, 1670, 2136, 2791, 3499, 4501, 5569, 7019, 8608, 10680, 12915, 15823, 18992, 22937, 27279, 32640, 38466, 45618, 53378, 62714, 72950, 85086, 98275, 113915, 130889, 150703

Offset

0,8

Links

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

Index entries for sequences related to partitions

Formula

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

Mathematica

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

Crossrefs

Cf. A008683, A309459, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.

Sequence in context: A308953 A143504 A322636 * A308926 A152043 A181585

Adjacent sequences: A309479 A309480 A309481 * A309483 A309484 A309485

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 04 2019

Status

approved