A294104 Sum of the differences of the larger and smaller parts in the partitions of n into two squarefree parts or two nonsquarefree parts.

0, 0, 1, 2, 1, 4, 8, 12, 8, 4, 10, 24, 22, 20, 29, 54, 33, 40, 31, 72, 37, 70, 54, 114, 68, 62, 74, 116, 97, 62, 114, 182, 136, 126, 147, 292, 175, 134, 180, 330, 214, 182, 227, 412, 273, 190, 209, 460, 343, 202, 156, 468, 392, 380, 156, 518, 394, 490, 303

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} (n - 2i) * [A008966(i) = A008966(n-i)], where [] is the Iverson bracket.

Maple

f:= n -> add(n-2*i, i = select(t -> numtheory:-issqrfree(t)=numtheory:-issqrfree(n-t), [$1..n/2])):
map(f, [$1..100]); # Robert Israel, Jun 12 2020

Mathematica

Table[Sum[(n - 2 k) KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[ n - k]^2], {k, Floor[n/2]}], {n, 80}]

Crossrefs

Cf. A008966, A294100.

Sequence in context: A156817 A008301 A363386 * A294061 A113820 A319479

Adjacent sequences: A294101 A294102 A294103 * A294105 A294106 A294107

Keyword

nonn,easy,look

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved