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

Author

Wesley Ivan Hurt, Oct 26 2017

Keywords

• nonn
• easy

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

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A294145, A294285.

Programs

Mathematica

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

PARI

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

Formula

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