

A098236


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


3



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: A277745 A030314 A269624 * A152978 A118121 A006968
Adjacent sequences: A098233 A098234 A098235 * A098237 A098238 A098239


KEYWORD

nonn,easy


AUTHOR

Ralf Stephan, Aug 31 2004


STATUS

approved



