

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
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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(2ni)^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 [&+[(1MoebiusMu(2*nk)^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*ni)^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



