A294100 Number of partitions of n into two squarefree parts or two nonsquarefree positive integer parts.

0, 1, 1, 2, 1, 2, 2, 4, 2, 2, 2, 5, 4, 3, 3, 7, 5, 5, 3, 8, 5, 6, 4, 10, 6, 6, 6, 10, 7, 6, 6, 12, 8, 9, 7, 17, 9, 8, 8, 16, 10, 9, 11, 18, 13, 9, 9, 19, 13, 10, 8, 21, 14, 14, 8, 20, 14, 15, 11, 22, 15, 14, 14, 23, 15, 14, 14, 27, 16, 17, 13, 33, 17, 18, 16

Offset

1,4

Comments

Number of distinct rectangles with both length and width squarefree or both nonsquarefree positive integers such that L + W = n, W <= L. For example, a(12) = 5; the rectangles are 1 X 11, 2 X 10, 4 X 8, 5 X 7, 6 X 6. - Wesley Ivan Hurt, Nov 04 2017

Links

Table of n, a(n) for n=1..75.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} [A008966(i) = A008966(n-i)], where [] is the Iverson bracket.

Mathematica

Table[Sum[KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[n - k]^2], {k, Floor[n/2]}], {n, 80}]

Prog

(PARI) a(n) = sum(i=1, n\2, issquarefree(i) == issquarefree(n-i)); \\ Michel Marcus, Nov 08 2017

Crossrefs

Cf. A008966, A294101.

Sequence in context: A050378 A225216 A161833 * A139318 A205779 A205551

Adjacent sequences: A294097 A294098 A294099 * A294101 A294102 A294103

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved