A368625 Characteristic function of non-refactorable numbers (A159973).

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

Offset: 1

Author

Wesley Ivan Hurt, Jan 01 2024

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Eric Weisstein's World of Mathematics, Refactorable Number
• Index entries for characteristic functions

Crossrefs

Cf. A000005, A033950 (refactorable numbers), A054008, A159973, A336040.

Programs

Mathematica

Table[(Ceiling[n/DivisorSigma[0, n]] - Floor[n/DivisorSigma[0, n]]), {n, 100}]

PARI

A368625(n) = !!(n%numdiv(n)); \\ Antti Karttunen, Jan 17 2025

Formula

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

a(n) = 1 - A336040(n).

a(n) = [A054008(n) > 0], where [ ] is the Iverson bracket. - Antti Karttunen, Jan 17 2025

Extensions

Data section extended up to a(105) by Antti Karttunen, Jan 17 2025