A302391 Number of partitions of 2n into two parts with at least one nonsquarefree part.

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

Links

Table of n, a(n) for n=1..69.

Index entries for sequences related to partitions

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

Cf. A008683, A013929, A280226, A294097.

Sequence in context: A354679 A307118 A052938 * A140114 A243852 A373701

Adjacent sequences: A302388 A302389 A302390 * A302392 A302393 A302394

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 06 2018

Status

approved