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A308768
Sum of the smallest parts of the partitions of n into 4 squarefree parts.
4
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
0,7
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).
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 23 2019
STATUS
approved