

A294100


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


2



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
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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(ni)], 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(ni)); \\ 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



