A373263 - OEIS

%I #10 May 31 2024 15:33:24

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

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

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

%N a(n) = 1 if A276085(n) == -1 (mod 3), otherwise 0, where A276085 is the primorial base log-function.

%H Antti Karttunen, <a href="/A373263/b373263.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) = [A373153(n) = -1], where [ ] is the Iverson bracket.

%F a(n) = [A007949(n)-A007814(n) == +1 (mod 3)].

%F a(n) = 1 - (A372573(n)+A373260(n)).

%o (PARI) A373263(n) = (1==((valuation(n,3)-valuation(n,2))%3));

%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 A373263(n) = (2==(A276085(n)%3));

%Y Characteristic function of A373262.

%Y Cf. A002110, A007814, A007949, A276085, A373153, A372573, A373260.

%K nonn

%O 1

%A _Antti Karttunen_, May 30 2024