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%I #8 Jun 08 2024 17:47:09
%S 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,
%T 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,
%U 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
%N 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.
%H Antti Karttunen, <a href="/A373481/b373481.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = [n==1 or A373480(n)==0], where [ ] is the Iverson bracket.
%t Array[Boole@ Divisible[If[#1 < 2, 0, #1 Total[#2/#1 & @@@ #2]], Total[Times @@@ #2]] & @@ {#, FactorInteger[#]} &, 120] (* _Michael De Vlieger_, Jun 08 2024 *)
%o (PARI)
%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373481(n) = (1==n || !(A003415(n)%A001414(n)));
%Y Characteristic function of A373482.
%Y Cf. A001414, A003415.
%K nonn
%O 1
%A _Antti Karttunen_, Jun 08 2024
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