%I #9 Jul 08 2024 16:41:09

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

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

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

%N a(n) = 1 if sigma(n) and sopfr(n) are both multiples of 3, otherwise 0, where sigma is the sum of divisors, and sopfr is the sum of prime factors with repetition.

%H Antti Karttunen, <a href="/A374222/b374222.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) = A079978(A374126(n)).

%F a(n) = (1-A353815(n)) * A373371(n).

%F a(3*n) = a(n).

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);

%o A374222(n) = (!(sigma(n)%3) && !(A001414(n)%3));

%Y Characteristic function of A374223.

%Y Cf. A000203, A001414, A079978, A353815, A373371, A374126.

%K nonn

%O 1

%A _Antti Karttunen_, Jul 08 2024