A090736 Number of positive integers <= n that can be expressed as a sum of 2 coprime 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, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19

Offset: 1

Author

Benoit Cloitre, Jan 18 2004

Keywords

• nonn

References

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

Links

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

Crossrefs

Cf. A008784, A064533, A090735.

Programs

Mathematica

Accumulate[Table[Boole[n > 1 && IntegerExponent[n, 2] < 2 && AllTrue[FactorInteger[n][[;; , 1]], Mod[#, 4] < 3 &]], {n, 1, 100}]] (* Amiram Eldar, May 08 2022 *)

PARI

a(n)=sum(i=1,n,if(sum(u=1,i,sum(v=1,u,if(abs(u^2+v^2-i)+abs(gcd(u,v)-1),0,1))),1,0))

Formula

a(n) is asymptotic to (3/(8*K))*n/sqrt(log(n)) where K is the Landau-Ramanujan constant (A064533).