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

0,1

Comments

Characteristic function of A001481.

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.

Formula

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

a(A022544(n)) = 0.

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

Multiplicative with a(p^e) = 0 if p == 3 (mod 4) and e is odd, and a(p^e) = 1 otherwise. - Amiram Eldar, Nov 21 2025

Mathematica

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

Prog

(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

Crossrefs

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

Cf. A000161, A022544.

Sequence in context: A011748 A145361 A189222 * A130304 A267533 A118274

Adjacent sequences: A229059 A229060 A229061 * A229063 A229064 A229065

Keyword

nonn,mult,easy

Author

Ralf Stephan, Sep 17 2013

Status

approved