login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A294101
Number of partitions of n into two parts such that one is squarefree and the other is nonsquarefree.
1
0, 0, 0, 0, 1, 1, 1, 0, 2, 3, 3, 1, 2, 4, 4, 1, 3, 4, 6, 2, 5, 5, 7, 2, 6, 7, 7, 4, 7, 9, 9, 4, 8, 8, 10, 1, 9, 11, 11, 4, 10, 12, 10, 4, 9, 14, 14, 5, 11, 15, 17, 5, 12, 13, 19, 8, 14, 14, 18, 8, 15, 17, 17, 9, 17, 19, 19, 7, 18, 18, 22, 3, 19, 19, 21, 8
OFFSET
1,9
FORMULA
a(n) = floor(n/2) - Sum_{i=1..floor(n/2)} [A008966(i) = A008966(n-i)], where [] is the Iverson bracket.
MATHEMATICA
Table[Floor[n/2] - Sum[KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[n - k]^2], {k, Floor[n/2]}], {n, 80}]
CROSSREFS
Sequence in context: A106589 A335490 A334290 * A051911 A106595 A181608
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 22 2017
STATUS
approved