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A098236
Number of ways to write n as the sum of two positive distinct squarefree numbers.
12
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
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
Sequence in context: A304111 A030314 A269624 * A152978 A118121 A006968
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Aug 31 2004
STATUS
approved