A360109 - OEIS

%I #9 Feb 01 2023 16:06:29

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

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

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

%N a(n) = 1 if n is not multiple of 4, but its arithmetic derivative is, otherwise 0.

%H Antti Karttunen, <a href="/A360109/b360109.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) = A166486(n) * A353494(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 A360109(n) = ((n%4)&&(0==(A003415(n)%4)));

%Y Characteristic function of A360110.

%Y Cf. A003415, A166486, A353494, A359828.

%Y After n=1 differs from A327932 for the first time at n=158, where a(158) = 0, while A327932(158) = 1.

%K nonn

%O 0

%A _Antti Karttunen_, Jan 31 2023