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

1,1

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A131736 A373254 A152228 * A086823 A228487 A295306

Adjacent sequences: A368622 A368623 A368624 * A368626 A368627 A368628

Keyword

nonn,easy,changed

Author

Wesley Ivan Hurt, Jan 01 2024

Extensions

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

Status

approved