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a(n) = 1 if the number of prime factors (with multiplicity) of n is a multiple of 3, and all of them are of the type 3m-1 (in A003627), otherwise 0.
5

%I #7 Jun 10 2024 17:44:40

%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 the number of prime factors (with multiplicity) of n is a multiple of 3, and all of them are of the type 3m-1 (in A003627), otherwise 0.

%H Antti Karttunen, <a href="/A373588/b373588.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) A373588(n) = if(bigomega(n)%3, 0, my(f = factor(n)); for(i = 1, #f~, if((f[i, 1]%3) != 2, return(0))); (1));

%Y Characteristic function of A373589.

%Y Cf. A001222, A003627, A004612, A145784.

%Y Differs from A373491 for the first time at n=343, where a(343) = 0, while A373491(343) = 1.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 10 2024