A229062 1 if n is representable as sum of two nonnegative squares, otherwise 0.

1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1

Offset: 0

Author

Ralf Stephan, Sep 17 2013

Keywords

• nonn
• mult

Comments

Characteristic function of A001481.

a(n) = 1 if A000161(n) > 0.

a(A022544(n)) = 0.

Multiplicative because A002654 is. - Andrew Howroyd, Aug 01 2018

For positive n, m = 2*a(n) + 1 is the smallest positive integer such that m * n is not a sum of two squares. - Peter Schorn, Dec 29 2023

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for characteristic functions

Crossrefs

Cf. A002654, A004018, A070176. Partial sums are in A102548.

Cf. A000161, A022544.

Programs

Mathematica

Join[{1},Table[If[SquaresR[2,n]>1,1,0],{n,120}]] (* Harvey P. Dale, Aug 25 2017 *)

PARI

a(n)=my(f=0); my(r=sqrtint(n)); forstep(i=r, 1, -1, if(issquare(n-i*i), f=1; break)); f

PARI

a(n)=if(0==n,1,(sumdiv(n, d,(d%4==1) - (d%4==3)) > 0)); \\ Andrew Howroyd, Aug 01 2018, the check for 0-argument added by Antti Karttunen, Apr 22 2022

Python

from sympy import factorint
def A229062(n): return int(all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(n).items())) # Chai Wah Wu, Jun 28 2022

Formula

a(n) = min{1, A004018(n)}. - N. J. A. Sloane, Jan 11 2020