A373143 - OEIS

%I #6 May 26 2024 18:42:12

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

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

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

%N a(n) = 1 if both A003415(n) and A276085(n) are multiples of 3, otherwise 0, where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

%C Question: Does this sequence have an asymptotic mean?

%H Antti Karttunen, <a href="/A373143/b373143.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) = A359430(n) * A372573(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 A002110(n) = prod(i=1,n,prime(i));

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

%o A373143(n) = (!(A003415(n)%3) && !(A276085(n)%3));

%Y Characteristic function of A373144.

%Y Cf.  A003415, A276085, A359430, A372573.

%K nonn

%O 1

%A _Antti Karttunen_, May 26 2024