A308906 Sum of the smallest parts in the partitions of n into 6 squarefree parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 9, 9, 12, 15, 21, 23, 31, 32, 45, 50, 61, 66, 87, 94, 114, 123, 154, 165, 199, 212, 261, 276, 323, 345, 418, 438, 507, 538, 637, 672, 771, 810, 947, 999, 1130, 1192, 1381, 1445, 1625, 1716, 1955, 2045, 2289, 2399, 2720

Offset

0,9

Links

Table of n, a(n) for n=0..56.

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

a(n) = A308903(n) - A308907(n) - A308908(n) - A308909(n) - A308910(n) - A308911(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[m*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, A308903, A308907, A308908, A308909, A308910, A308911.

Sequence in context: A369708 A085570 A059850 * A337823 A051630 A050045

Adjacent sequences: A308903 A308904 A308905 * A308907 A308908 A308909

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 29 2019

Status

approved