A098236 Number of ways to write n as the sum of two positive distinct squarefree numbers.
0, 0, 1, 1, 1, 1, 2, 3, 2, 1, 2, 3, 3, 2, 3, 5, 4, 4, 3, 5, 4, 4, 4, 7, 5, 4, 5, 6, 5, 4, 5, 8, 6, 6, 6, 11, 7, 6, 7, 11, 8, 7, 9, 12, 10, 7, 8, 13, 10, 8, 7, 13, 10, 10, 7, 13, 10, 10, 9, 14, 11, 10, 11, 15, 11, 10, 11, 17, 12, 12, 11, 21, 13, 13, 13, 19, 14, 12, 14, 20, 16, 12, 13, 21
Offset: 1
Programs
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Maple
with(numtheory): A098236:=n->add(mobius(i)^2*mobius(n-i)^2, i=1..floor(n/2)-((n+1) mod 2)): seq(A098236(n), n=1..150); # Wesley Ivan Hurt, Oct 29 2017
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Mathematica
Table[Sum[MoebiusMu[i]^2*MoebiusMu[n - i]^2, {i, Floor[(n-1)/2]}], {n, 80}] (* Wesley Ivan Hurt, Oct 26 2017 *) -
PARI
a(n) = sum(i=1, n\2-(n+1)%2, moebius(i)^2*moebius(n-i)^2); \\ Michel Marcus, Oct 27 2017
Formula
a(n) = Sum_{k=1..floor((n-1)/2)} mu(k)^2 * mu(n-k)^2. - Wesley Ivan Hurt, Oct 26 2017
Comments