A393067 - OEIS

%I #7 Jan 31 2026 16:50:23

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

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

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

%N a(n) = 1 if A276086(A003415(n)) <= n, otherwise 0, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%H Antti Karttunen, <a href="/A393067/b393067.txt">Table of n, a(n) for n = 1..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>.

%o (PARI) A393067(n) = if(!n, 0, my(f=factor(n), u = n*sum(i=1, #f~, f[i, 2]/f[i, 1]), m=1, p=2); while(u, m *= (p^(u%p)); if(m>n, return(0)); u \= p; p = nextprime(1+p)); (1));

%Y Characteristic function of A392867.

%Y Cf. A003415, A276086.

%Y Cf. also A393068.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 31 2026