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A373596
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.
4
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, 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, 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
OFFSET
1
PROG
(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)));
CROSSREFS
Characteristic function of A373597.
Differs from A373588 for the first time at n=343, where a(343) = 1, while A373588(343) = 0.
Differs from A373491 for the first time at n=1323, where a(1323) = 0, while A373491(1323) = 1.
Cf. also A353557 (roughly analogous sequence for k=2, instead of k=3).
Sequence in context: A014744 A373491 A373588 * A373472 A373493 A014646
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 10 2024
STATUS
approved