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A280226
Number of partitions of 2n into two squarefree parts.
11
1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 5, 7, 5, 8, 7, 11, 7, 11, 8, 13, 8, 13, 8, 14, 10, 13, 11, 15, 11, 15, 11, 18, 13, 21, 14, 20, 13, 20, 13, 22, 14, 23, 17, 23, 17, 24, 17, 25, 18, 26, 19, 31, 19, 29, 20, 31, 20, 31, 20, 33, 23, 30, 23, 32, 23, 32, 23, 35, 24, 41, 25, 39
OFFSET
1,2
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
with(numtheory): A280226:=n->sum(mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280226(n), n=1..100);
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 29 2016
STATUS
approved