

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

Table of n, a(n) for n=1..73.
Index entries for sequences related to partitions


FORMULA

a(n) = n  Sum_{i=1..n} [c(i) = c(2*ni)], where [] is the Iverson bracket and c is the squarefree characteristic (A008966).
a(n) = Sum_{i=1..n} mu(i)^2 * (1mu(2*ni)^2) + (1mu(i)^2) * mu(2*ni)^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



