A296084 a(1) = 0 and for n > 1, a(n) = 1 if tau(n)-1 divides sigma(n)-1, 0 otherwise. Here tau = A000005, sigma = A000203.

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

Offset

1

Comments

Also number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 3 (equivalently, i*n is the square of a prime). - N. J. A. Sloane, Nov 11 2020

Links

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

Index entries for characteristic functions

Formula

a(n) = 1 iff A296082(n) = 1.

Mathematica

Join[{0}, Table[If[Divisible[DivisorSigma[1, n]-1, DivisorSigma[0, n]-1], 1, 0], {n, 2, 120}]] (* Harvey P. Dale, Dec 15 2018 *)

Prog

(PARI) A296084(n) = if(1==n, 0, !((sigma(n)-1)%(numdiv(n)-1)));
(Python)
from math import prod
from sympy import factorint
def A296084(n):
    f = factorint(n).items()
    return int(not (prod((p**(e+1)-1)//(p-1) for p, e in f)-1)%(prod(e+1 for p, e in f)-1)) if n>1 else 0 # Chai Wah Wu, Oct 14 2023

Crossrefs

Cf. A000005, A000203, A032741, A039653, A296082.

Characteristic function of A284288.

Sequence in context: A100656 A285274 A189081 * A302777 A324828 A332823

Adjacent sequences: A296081 A296082 A296083 * A296085 A296086 A296087

Keyword

nonn

Author

Antti Karttunen, Dec 05 2017

Status

approved