A373486 - OEIS

%I #6 Jun 09 2024 14:04:39

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

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

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

%N a(n) = 1 if A276085(n) is a multiple of A003415(n), otherwise 0, where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

%H Antti Karttunen, <a href="/A373486/b373486.txt">Table of n, a(n) for n = 1..100000</a>

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

%F a(n) = [n==1 or A373148(n)==0], where [ ] is the Iverson bracket.

%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 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };

%o A373486(n) = (1==n || !(A276085(n)%A003415(n)));

%Y Characteristic function of A373487.

%Y Cf. A003415, A276085, A373148, A373488.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 09 2024