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 A302391 Number of partitions of 2n into two parts with at least one nonsquarefree part. 0
 0, 0, 1, 1, 3, 2, 4, 3, 5, 4, 6, 5, 8, 7, 10, 8, 10, 7, 12, 9, 13, 9, 15, 11, 17, 12, 17, 15, 18, 15, 20, 17, 22, 16, 22, 15, 23, 18, 26, 20, 28, 20, 29, 21, 28, 23, 30, 24, 32, 25, 33, 26, 34, 23, 36, 27, 37, 27, 39, 29, 41, 29, 40, 34, 42, 34, 44, 36, 46 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS FORMULA a(n) = Sum_{i=1..n} 1 - mu(2n-i)^2 * mu(i)^2, where mu = A008683. MATHEMATICA Table[Sum[1 - MoebiusMu[2 n - i]^2*MoebiusMu[i]^2, {i, n}], {n, 100}] PROG (MAGMA [&+[(1-MoebiusMu(2*n-k)^2*MoebiusMu(k)^2): k in [1..n]]: n in [1..70]]; // Vincenzo Librandi, Apr 09 2018 (PARI) a(n) = sum(i=1, n, 1 - moebius(2*n-i)^2*moebius(i)^2); \\ Michel Marcus, Apr 09 2018 CROSSREFS Cf. A008683, A013929, A280226, A294097. Sequence in context: A316141 A119707 A052938 * A140114 A243852 A025532 Adjacent sequences:  A302388 A302389 A302390 * A302392 A302393 A302394 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Apr 06 2018 STATUS approved

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Last modified January 22 18:06 EST 2019. Contains 319365 sequences. (Running on oeis4.)