A340755 Number of partitions of n into 4 parts such that the sum of the smallest two parts and the sum of the largest two parts are both squarefree.

0, 0, 0, 0, 1, 1, 0, 2, 4, 5, 2, 1, 7, 10, 4, 11, 23, 22, 16, 26, 35, 31, 28, 28, 52, 48, 43, 49, 80, 73, 34, 58, 105, 107, 70, 99, 195, 157, 89, 159, 258, 227, 164, 238, 374, 327, 251, 282, 480, 404, 306, 306, 539, 481, 402, 290, 566, 528, 472, 352, 630, 582, 495, 500, 766, 648, 598, 546, 1033, 733, 772, 616, 1428, 873, 952, 938, 1515, 1111, 1028, 1239, 1742

Offset

0,8

Links

Table of n, a(n) for n=0..80.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[Sum[Sum[MoebiusMu[k + j]^2*MoebiusMu[n - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]

Crossrefs

Cf. A008683 (mu).

Sequence in context: A075884 A030750 A286147 * A369772 A059215 A125142

Adjacent sequences: A340752 A340753 A340754 * A340756 A340757 A340758

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 19 2021

Status

approved