A373481 a(n) = 1 if A003415(n) is a multiple of A001414(n), otherwise 0, where A003415 is the arithmetic derivative, and A001414 is the sum of prime factors with multiplicity.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = [n==1 or A373480(n)==0], where [ ] is the Iverson bracket.

Mathematica

Array[Boole@ Divisible[If[#1 < 2, 0, #1  Total[#2/#1 & @@@ #2]], Total[Times @@@ #2]] & @@ {#, FactorInteger[#]} &, 120] (* Michael De Vlieger, Jun 08 2024 *)

Prog

(PARI)
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A373481(n) = (1==n || !(A003415(n)%A001414(n)));

Crossrefs

Characteristic function of A373482.

Cf. A001414, A003415.

Sequence in context: A267612 A242252 A100810 * A174889 A005171 A283265

Adjacent sequences: A373478 A373479 A373480 * A373482 A373483 A373484

Keyword

nonn

Author

Antti Karttunen, Jun 08 2024

Status

approved