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a(n) = 1 if n and A327860(n) are both multiples of 3, where A327860 is the arithmetic derivative of the primorial base exp-function.
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%I #19 Jun 18 2024 16:19:22

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N a(n) = 1 if n and A327860(n) are both multiples of 3, where A327860 is the arithmetic derivative of the primorial base exp-function.

%C Apparently the asymptotic mean is 1/18, although this is not a characteristic function for the multiples of 18.

%H Antti Karttunen, <a href="/A373598/b373598.txt">Table of n, a(n) for n = 0..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = [A351083(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

%F a(n) = A079978(n) * A369653(n).

%F a(n) = A373143(A276086(n)).

%F If a(x) = a(y) = A329041(x,y) = 1, then a(x+y) = 1 also. See explanation in the comments of A373599.

%o (PARI)

%o A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };

%o A373598(n) = (!(n%3) && !(A327860(n)%3));

%Y Characteristic function of A373599.

%Y Cf. A079978, A276086, A327860, A329041, A351083, A369653, A373143.

%K nonn

%O 0

%A _Antti Karttunen_, Jun 18 2024