OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{i=1..n} mu(i)^2 * mu(2n-i)^2, where mu is the Möbius function (A008683).
a(n) = n - A302391(n). - Wesley Ivan Hurt, Dec 11 2023
EXAMPLE
From Wesley Ivan Hurt, Feb 20 2018: (Start)
a(5) = 2; there are two partitions of 2*5 = 10 into two squarefree parts: (7,3), (5,5).
a(6) = 4; there are four partitions of 2*6 = 12 into two squarefree parts: (11,1), (10,2), (7,5), (6,6).
a(7) = 3; there are three partitions of 2*7 = 14 into two squarefree parts: (13,1), (11,3), (7,7).
a(8) = 5; there are five partitions of 2*8 = 16 into two squarefree parts: (15,1), (14,2), (13,3), (11,5), (10,6). (End)
MAPLE
MATHEMATICA
f[n_] := Sum[(MoebiusMu[i]*MoebiusMu[2n -i])^2, {i, n}]; Array[f, 74] (* Robert G. Wilson v, Dec 29 2016 *)
PROG
(PARI) a(n)=sum(i=1, n, issquarefree(i) && issquarefree(2*n-i)) \\ Charles R Greathouse IV, Nov 05 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 29 2016
STATUS
approved