A308768 Sum of the smallest parts of the partitions of n into 4 squarefree parts.

0, 0, 0, 0, 1, 1, 2, 2, 5, 5, 7, 8, 12, 11, 16, 16, 23, 23, 30, 32, 44, 43, 56, 57, 72, 72, 90, 87, 114, 112, 135, 137, 169, 164, 197, 196, 233, 238, 282, 276, 337, 332, 381, 378, 454, 447, 525, 523, 606, 609, 698, 678, 800, 799, 907, 895, 1050, 1022, 1157

Offset: 0

Author

Wesley Ivan Hurt, Jun 23 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A308762, A308767, A308769, A308770, A308783.

Programs

Mathematica

Table[Sum[Sum[Sum[k * MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2* MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

Formula

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

a(n) = A308783(n) - A308762(n) - A308769(n) - A308770(n).