A336040 Characteristic function of refactorable numbers (A033950).

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

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Refactorable Number

Index entries for characteristic functions

Formula

a(n) = 1 - ceiling(n/d(n)) + floor(n/d(n)), where d(n) is the number of divisors of n (A000005).

a(n) = [A054008(n) == 0], where [ ] is the Iverson bracket. - Antti Karttunen, Nov 24 2021

a(p) = 0 for odd primes p. - Wesley Ivan Hurt, Nov 28 2021

Example

a(1) = 1 since d(1) = 1 and 1 divides 1.
a(2) = 1 since d(2) = 2 and 2 divides 2.
a(3) = 0 since d(3) = 2, but 2 does not divide 3.

Mathematica

a[n_] := Boole @ Divisible[n, DivisorSigma[0, n]]; Array[a, 100] (* Amiram Eldar, Jul 08 2020 *)

Prog

(PARI) a(n) = n%numdiv(n) == 0; \\ Michel Marcus, Jul 07 2020

Crossrefs

Cf. A000005, A033950, A054008, A336041 (inverse Möbius transform), A335182, A335665, A349322.

Sequence in context: A011654 A016348 A015556 * A359769 A359770 A015780

Adjacent sequences: A336037 A336038 A336039 * A336041 A336042 A336043

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jul 07 2020

Status

approved