A308903 Sum of all the parts in the partitions of n into 6 squarefree parts.

0, 0, 0, 0, 0, 0, 6, 7, 16, 18, 40, 55, 96, 104, 154, 195, 288, 323, 450, 513, 720, 819, 1056, 1196, 1584, 1750, 2210, 2457, 3108, 3393, 4170, 4588, 5632, 6105, 7276, 7945, 9576, 10286, 12084, 13104, 15480, 16605, 19278, 20726, 24200, 25830, 29624, 31772

Offset

0,7

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

Formula

a(n) = 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), where mu is the Möbius function (A008683).

a(n) = n * A308902(n).

a(n) = A308906(n) + A308907(n) + A308908(n) + A308909(n) + A308910(n) + A308911(n).

Mathematica

Table[n*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}]

Crossrefs

Cf. A008683, A308902, A308906, A308907, A308908, A308909, A308910, A308911.

Sequence in context: A008538 A000870 A315844 * A315845 A322638 A309481

Adjacent sequences: A308900 A308901 A308902 * A308904 A308905 A308906

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 29 2019

Status

approved