A355816 a(n) = 1 if n and sigma(n) are relatively prime, and n has at least two distinct prime factors, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

a(n) = A143731(n) * A325964(n).

a(n) = [A001221(n) > 1] * [1 == A009194(n)], where [ ] is the Iverson bracket.

Mathematica

a[n_] := If[!PrimePowerQ[n] && CoprimeQ[n, DivisorSigma[1, n]], 1, 0]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jul 18 2022 *)

Prog

(PARI) A355816(n) = ((omega(n)>1) && (1==gcd(n, sigma(n))));

Crossrefs

Characteristic function of A095738, numbers that are coprime to sigma but are not prime powers.

Cf. A001221, A009194, A143731, A325964.

Sequence in context: A011736 A085982 A011735 * A353483 A353809 A353808

Adjacent sequences: A355813 A355814 A355815 * A355817 A355818 A355819

Keyword

nonn

Author

Antti Karttunen, Jul 18 2022

Status

approved