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 A294098 Number of partitions of 2n into two parts such that one part is squarefree and the other part is nonsquarefree. 1
 0, 0, 1, 0, 3, 1, 4, 1, 4, 2, 5, 2, 7, 4, 9, 4, 8, 1, 11, 4, 12, 4, 14, 5, 15, 5, 13, 8, 14, 8, 17, 9, 19, 7, 18, 3, 19, 8, 23, 10, 25, 9, 26, 9, 22, 12, 25, 12, 27, 11, 27, 12, 28, 5, 31, 12, 32, 12, 34, 13, 36, 12, 31, 18, 34, 18, 37, 19, 39, 17, 40, 7, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS FORMULA a(n) = n - Sum_{i=1..n} [c(i) = c(2*n-i)], where [] is the Iverson bracket and c is the squarefree characteristic (A008966). a(n) = Sum_{i=1..n} mu(i)^2 * (1-mu(2*n-i)^2) + (1-mu(i)^2) * mu(2*n-i)^2, where mu is the Möbius function (A008683). - Wesley Ivan Hurt, Nov 18 2017 MATHEMATICA Table[n - Sum[KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[2 n - k]^2], {k, n}], {n, 80}] CROSSREFS Cf. A008683, A008966, A294097. Sequence in context: A240698 A010602 A120731 * A087477 A029212 A035687 Adjacent sequences:  A294095 A294096 A294097 * A294099 A294100 A294101 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Oct 22 2017 STATUS approved

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Last modified July 25 19:34 EDT 2021. Contains 346291 sequences. (Running on oeis4.)