%I #11 Jan 10 2024 23:59:05

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

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

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

%N a(n) = 1 if k-th arithmetic derivative of A276086(n) is zero for some k, otherwise 0.

%C a(n) = 1 if A276086(n) is in A099308, 0 otherwise.

%C Question: Does the sequence have asymptotic mean? See also A328307 and A351071. - _Antti Karttunen_, Jan 10 2024

%H Antti Karttunen, <a href="/A328306/b328306.txt">Table of n, a(n) for n = 0..65537</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) = A328308(A276086(n)).

%F For n > 0, a(n) <= A368916(n). - _Antti Karttunen_, Jan 10 2024

%o (PARI)

%o A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i,2]>=f[i,1],return(0), s += f[i, 2]/f[i, 1])); (n*s));

%o A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };

%o A328308(n) = if(!n,1, while(n>1, n = A003415checked(n)); (n));

%o A328306(n) = A328308(A276086(n));

%Y Characteristic function of A328116.

%Y Cf. A003415, A099308, A276086, A328307 (partial sums), A328308, A351071, A368916.

%K nonn

%O 0

%A _Antti Karttunen_, Oct 12 2019