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

1,7

Comments

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

Links

Table of n, a(n) for n=1..84.

Formula

a(n) = Sum_{k=1..floor((n-1)/2)} mu(k)^2 * mu(n-k)^2. - Wesley Ivan Hurt, Oct 26 2017

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

Mathematica

Table[Sum[MoebiusMu[i]^2*MoebiusMu[n - i]^2, {i, Floor[(n-1)/2]}], {n, 80}] (* Wesley Ivan Hurt, Oct 26 2017 *)

Prog

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

Crossrefs

Cf. A005117, A098235.

Sequence in context: A304111 A030314 A269624 * A152978 A118121 A006968

Adjacent sequences: A098233 A098234 A098235 * A098237 A098238 A098239

Keyword

nonn,easy

Author

Ralf Stephan, Aug 31 2004

Status

approved