A349167 a(n) = 1 if sigma(n) and A003961(n) are relatively prime, otherwise 0.

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

Offset

1

Comments

Characteristic function of A349165.

Links

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

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = 1 iff A342671(n) == 1, otherwise a(n) = 0.

Mathematica

f1[p_, e_] := NextPrime[p]^e; f2[p_, e_] := (p^(e + 1) - 1)/(p - 1); a[1] = 1; a[n_] := Boole @ CoprimeQ[Times @@ f1 @@@ (f = FactorInteger[n]), Times @@ f2 @@@ f]; Array[a, 100] (* Amiram Eldar, Nov 28 2021 *)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A349167(n) = (1==gcd(sigma(n), A003961(n)));

Crossrefs

Cf. A000203, A003961, A342671, A349163, A349165, A349166.

Cf. also A348737.

Sequence in context: A259024 A323045 A104106 * A141260 A029883 A035263

Adjacent sequences: A349164 A349165 A349166 * A349168 A349169 A349170

Keyword

nonn

Author

Antti Karttunen, Nov 10 2021

Status

approved