A090735 Number of positive squarefree numbers <= n that can be expressed as a sum of 2 squares > 0.

0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17

Offset

1,5

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 100

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) is asymptotic to (6K/Pi^2)*n/sqrt(log(n)) where K is the Landau-Ramanujan constant (A064533).

Mathematica

Accumulate[Table[Boole[n > 1 && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;; , 1]], Mod[#, 4] < 3 &]], {n, 1, 100}] ] (* Amiram Eldar, May 08 2022 *)

Prog

(PARI) a(n)=sum(i=1, n, issquarefree(i)*if(sum(u=1, i, sum(v=1, u, if(u^2+v^2-i, 0, 1))), 1, 0))

Crossrefs

Cf. A005117, A020893, A064533, A090736.

Sequence in context: A131849 A362344 A244479 * A090736 A094999 A280951

Adjacent sequences: A090732 A090733 A090734 * A090736 A090737 A090738

Keyword

nonn

Author

Benoit Cloitre, Jan 18 2004

Status

approved