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a(n) = 1 if the arithmetic derivative (A003415) of n is a prime, otherwise 0.
5

%I #5 Feb 28 2021 20:29:38

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

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

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

%N a(n) = 1 if the arithmetic derivative (A003415) of n is a prime, otherwise 0.

%H Antti Karttunen, <a href="/A341995/b341995.txt">Table of n, a(n) for n = 0..65537</a>

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

%F a(n) = A010051(A003415(n)).

%F For all n > 0, a(n) <= A341994(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 A341995(n) = isprime(A003415(n));

%Y Characteristic function of A157037.

%Y Cf. A003415, A010051, A341994.

%K nonn

%O 0

%A _Antti Karttunen_, Feb 28 2021