A294284 Sum of the smaller parts of the partitions of n into two distinct parts with larger part squarefree.

0, 0, 1, 1, 2, 1, 3, 6, 9, 7, 10, 8, 11, 8, 12, 17, 22, 28, 34, 31, 37, 33, 40, 48, 56, 51, 59, 53, 60, 53, 61, 70, 79, 72, 82, 93, 104, 97, 109, 122, 135, 128, 142, 135, 149, 140, 154, 169, 184, 199, 214, 204, 219, 235, 251, 268, 285, 274, 292, 281

Offset

1,5

Comments

Sum of the widths of the distinct rectangles with squarefree length and positive integer width such that L + W = n, W < L. For example, a(13) = 11; the rectangles are 2 X 11, 3 X 10, 6 X 7. The sum of the widths is then 2 + 3 + 6 = 11. - Wesley Ivan Hurt, Nov 12 2017

Links

Table of n, a(n) for n=1..60.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[i*MoebiusMu[n - i]^2, {i, Floor[(n-1)/2]}], {n, 60}]

Prog

(PARI) a(n) = sum(i=1, (n-1)\2, i*moebius(n-i)^2); \\ Michel Marcus, Nov 05 2017

Crossrefs

Cf. A008683, A294145, A294285.

Sequence in context: A053225 A050043 A113396 * A295678 A057925 A086964

Adjacent sequences: A294281 A294282 A294283 * A294285 A294286 A294287

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 26 2017

Status

approved