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A302391
Number of partitions of 2n into two parts with at least one nonsquarefree part.
1
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
OFFSET
1,5
FORMULA
a(n) = Sum_{i=1..n} 1 - mu(2n-i)^2 * mu(i)^2, where mu is the Möbius function (A008683).
a(n) = n - A280226(n). - Wesley Ivan Hurt, Dec 11 2023
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 06 2018
STATUS
approved