A319691 - OEIS

A319691

a(n) = 1 if n is either 1 or divisible only by primes congruent to 1 mod 3, 0 otherwise.

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

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OFFSET

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

FORMULA

a(n) = A319690(n) mod 2.

Fully multiplicative with a(p) = 1 if p is a prime of the form 3k+1, otherwise a(p) = 0.

MATHEMATICA

Table[If[AllTrue[FactorInteger[n][[All, 1]], Mod[#, 3]==1&], 1, 0], {n, 120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 26 2020 *)

PROG

(PARI) A319691(n) = factorback(apply(p -> ((p%3)%2), factor(n)[, 1]));

CROSSREFS

Characteristic function of A004611.

Cf. A319690.

Sequence in context: A015989 A267417 A014189 * A079979 A288711 A347312

Adjacent sequences: A319688 A319689 A319690 * A319692 A319693 A319694

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Oct 04 2018

STATUS

approved