OFFSET
1,5
FORMULA
a(n) = n - Sum_{i=1..n} [c(i) = c(2*n-i)], where [] is the Iverson bracket and c is the squarefree characteristic (A008966).
a(n) = Sum_{i=1..n} mu(i)^2 * (1-mu(2*n-i)^2) + (1-mu(i)^2) * mu(2*n-i)^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}]
Table[Count[IntegerPartitions[2n, {2}], _?(Total[Boole[ SquareFreeQ/@#]] == 1&)], {n, 80}] (* Harvey P. Dale, Jul 27 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 22 2017
STATUS
approved