A353816 a(n) = 1 if n is a number of the form x^2 + xy + y^2, otherwise 0.

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

Offset

0

Comments

a(n) = 1 iff in the prime factorization of n, all primes == 2 (mod 3) occur to even powers.

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Formula

a(n) = [A088534(n) > 0], where [ ] is the Iverson bracket.

a(n) >= A353815(n).

Multiplicative with a(p^e) = 0 if p == 2 (mod 3) and e is odd, and a(p^e) = 1 in all other cases. - Antti Karttunen, Jul 04 2024

Prog

(PARI) A353816(n) = if(!n, 1, my(f=factor(n), flag=1); for(i=1, #f~, if(Mod(f[i, 1], 3)==2 && Mod(f[i, 2], 2)==1, flag=0)); (flag)); \\ After function isA003136 in A003136.
(PARI) A353816(n) = if(!n, 1, my(f=factor(n)); prod(i=1, #f~, (2!=(f[i, 1]%3) || (1+f[i, 2])%2))); \\ Antti Karttunen, Jul 04 2024

Crossrefs

Characteristic function of A003136.

Cf. A088534, A353815.

Sequence in context: A278513 A134842 A167753 * A141727 A298952 A123594

Adjacent sequences: A353813 A353814 A353815 * A353817 A353818 A353819

Keyword

nonn,mult

Author

Antti Karttunen, May 15 2022

Extensions

Keyword:mult added by Antti Karttunen, Jul 04 2024

Status

approved