A374041 - OEIS

%I #10 Jun 27 2024 18:13:06

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

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

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

%N a(n) = 1 if A276085(n) and A328768(n) are both multiples of 3, otherwise 0, where A276085 is the primorial base log-function, and A328768 is the first primorial based variant of arithmetic derivative.

%H Antti Karttunen, <a href="/A374041/b374041.txt">Table of n, a(n) for n = 1..100000</a>

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

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A372573(n) * A373991(n).

%F a(n) = A372573(n) * [A007949(n) != 1], where [ ] is the Iverson bracket.

%F a(n) = A079978(A374031(n)).

%o (PARI)

%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 A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));

%o A374041(n) = (!(A276085(n)%3) && !(A328768(n)%3));

%o (PARI) A374041(n) = { my(v2 = valuation(n, 2), v3 = valuation(n, 3)); ((v3 != 1) && 0==((v2-v3)%3)); };

%Y Characteristic function of A374042.

%Y Cf. A002110, A079978, A276085, A328768, A372573, A373991, A374031.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 26 2024