A358771 - OEIS

%I #9 Dec 01 2022 22:31:08

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

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

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

%N a(n) = 1 if the arithmetic derivative of n is of the form 4k+1, otherwise 0.

%H Antti Karttunen, <a href="/A358771/b358771.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) = [A003415(n) == 1 (mod 4)], where [ ] is the Iverson bracket.

%F a(n) = A165560(n) - A358773(n).

%F a(n) >= A010051(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 A358771(n) = (1==(A003415(n)%4));

%Y Characteristic function of A358772.

%Y Cf. A003415, A010051, A010873, A165560.

%Y Cf. also A353494, A353495, A358773 and A358751 [= a(A003961(n))].

%K nonn

%O 0

%A _Antti Karttunen_, Dec 01 2022