%I #11 Feb 10 2024 09:22:20

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

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

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

%N a(n) = 1 if n is not multiple of 5, but its arithmetic derivative is, otherwise 0.

%C Conjecture: the asymptotic mean of this sequence is (4/5)*(1/5) = 4/25 = 0.16. Compare to A369967 and the conjecture at A369658.

%H Antti Karttunen, <a href="/A369968/b369968.txt">Table of n, a(n) for n = 0..100000</a>

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

%F a(n) = A011558(n) * A369967(n).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A369968(n) = ((n%5)&&(0==(A003415(n)%5)));

%Y Characteristic function of A369969.

%Y Cf. A003415, A011558, A369967.

%Y Cf. also A353557, A369658, A360109, for cases k = 2, 3, 4 of the characteristic functions for nonmultiples of k whose arithmetic derivative is multiple of k.

%K nonn

%O 0

%A _Antti Karttunen_, Feb 10 2024