

A098236


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


11



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
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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_{i=1..floor(n/2)((n+1) mod 2)} mu(i)^2 * mu(ni)^2.  Wesley Ivan Hurt, Oct 26 2017


MAPLE

with(numtheory): A098236:=n>add(mobius(i)^2*mobius(ni)^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/2]  Mod[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(ni)^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



