A373596 - OEIS

%I #9 Jun 11 2024 08:31:01

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

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

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

%N a(n) = 1 if n is a non-multiple of 3 whose multiplicies of prime factors of types 3m-1 and 3m+1 are both multiples of 3, otherwise 0.

%H Antti Karttunen, <a href="/A373596/b373596.txt">Table of n, a(n) for n = 1..100000</a>

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

%o (PARI) A373596(n) = if(!(n%3) || bigomega(n)%3, 0, my(f = factor(n),m1=0,m2=0); for(i = 1, #f~, if(1==(f[i, 1]%3), m1 += f[i,2], m2 += f[i,2])); (0==(gcd(m1,m2)%3)));

%Y Characteristic function of A373597.

%Y Differs from A373588 for the first time at n=343, where a(343) = 1, while A373588(343) = 0.

%Y Differs from A373491 for the first time at n=1323, where a(1323) = 0, while A373491(1323) = 1.

%Y Cf. also A353557 (roughly analogous sequence for k=2, instead of k=3).

%K nonn

%O 1

%A _Antti Karttunen_, Jun 10 2024