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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.
3
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
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.
Sequence in context: A267612 A242252 A100810 * A174889 A005171 A283265
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 08 2024
STATUS
approved