A374197 a(n) is 1 if the minimum value of A017666 that it obtains among divisors of n larger than 1 is 1, otherwise 0. By convention a(1) = 1.

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

Offset

1

Links

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

Index entries for characteristic functions.

Formula

a(n) = [A374196(n) == 1], where [ ] is the Iverson bracket.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{s subset of A007691 \ {1}} (-1)^(card(s)+1)/LCM(s) = 0.1916963... . - Amiram Eldar, Apr 16 2025

Mathematica

a[n_] := Boole[n == 1 || AnyTrue[Rest[Divisors[n]], IntegerQ[DivisorSigma[-1, #]] &]]; Array[a, 120] (* Amiram Eldar, Apr 16 2025 *)

Prog

(PARI) A374197(n) = { my(m=0, x); fordiv(n, d, if(d>1, x = denominator(sigma(d)/d); if(!m || x<m, m=x))); (!m || (1==m)); };

Crossrefs

Characteristic function of A374198.

Cf. A007691, A017666, A374196.

Sequence in context: A348033 A327153 A390095 * A133943 A014084 A014159

Adjacent sequences: A374194 A374195 A374196 * A374198 A374199 A374200

Keyword

nonn

Author

Antti Karttunen, Jul 07 2024

Status

approved