A360128 a(n) = 1 if there are no divisors d>1 of n such that also d+1 is a divisor of n, otherwise 0.

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

Offset

1

Comments

It appears that all zero terms are even indexed. - Harvey P. Dale, Feb 14 2025

Links

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

Index entries for characteristic functions

Formula

a(n) = [A088722(n) == 0], where [ ] is the Iverson bracket.

a(n) = [A129308(n) < 2] = [A328457(n) < 2].

Mathematica

Table[If[FreeQ[Differences[Rest[Divisors[n]]], 1], 1, 0], {n, 150}] (* Harvey P. Dale, Feb 14 2025 *)

Prog

(PARI) A360128(n) = !sumdiv(n, d, (d>1)&&!(n%(d+1)));

Crossrefs

Characteristic function of A088725.

Cf. A088722, A129308, A328457, A360129.

Sequence in context: A336834 A356173 A294934 * A174340 A380545 A300294

Adjacent sequences: A360125 A360126 A360127 * A360129 A360130 A360131

Keyword

nonn

Author

Antti Karttunen, Feb 20 2023

Status

approved