A370122 - OEIS

%I #10 Feb 10 2024 18:53:42

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

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

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

%N a(n) = 1 if the second arithmetic derivative of n is a multiple of 3, otherwise 0.

%H Antti Karttunen, <a href="/A370122/b370122.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) = A079978(A068346(n)) = A359430(A003415(n)).

%F a(n) = A370118(n) + A369658(A003415(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 A068346(n) = A003415(A003415(n));

%o A370122(n) = (0==(A068346(n)%3));

%Y Characteristic function of A370123.

%Y Cf. A003415, A068346, A079978, A359430, A369658, A370118.

%K nonn

%O 0

%A _Antti Karttunen_, Feb 10 2024