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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)