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A098236 Number of ways to write n as the sum of two positive distinct squarefree numbers. 11

%I

%S 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,

%T 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,

%U 10,11,15,11,10,11,17,12,12,11,21,13,13,13,19,14,12,14,20,16,12,13,21

%N Number of ways to write n as the sum of two positive distinct squarefree numbers.

%C Number of distinct rectangles with squarefree length and width such that L + W = n, W < L. - _Wesley Ivan Hurt_, Oct 29 2017

%F a(n) = Sum_{i=1..floor(n/2)-((n+1) mod 2)} mu(i)^2 * mu(n-i)^2. - _Wesley Ivan Hurt_, Oct 26 2017

%p 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

%t Table[Sum[MoebiusMu[i]^2*MoebiusMu[n - i]^2, {i, Floor[n/2] - Mod[n + 1, 2]}], {n, 80}] (* _Wesley Ivan Hurt_, Oct 26 2017 *)

%o (PARI) a(n) = sum(i=1, n\2-(n+1)%2, moebius(i)^2*moebius(n-i)^2); \\ _Michel Marcus_, Oct 27 2017

%Y Cf. A005117, A098235.

%K nonn,easy

%O 1,7

%A _Ralf Stephan_, Aug 31 2004

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)