A373483 - OEIS

%I #8 Jun 09 2024 14:04:47

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

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

%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 A083345(n) and A276085(n) are both multiples of 3, otherwise 0, where A276085 is fully additive with a(p) = p#/p, and A083345 is the numerator of the fully additive function with a(p) = 1/p.

%H Antti Karttunen, <a href="/A373483/b373483.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) = A369643(n) * A372573(n).

%F a(n) = [A373485(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

%F a(n) <= A373143(n).

%o (PARI)

%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, 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 A373483(n) = (!(A083345(n)%3) && !(A276085(n)%3));

%Y Characteristic function of A373484.

%Y Cf. A083345, A276085, A369643, A372573, A373143, A373485.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 09 2024