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A359430
a(n) = 1 if the arithmetic derivative of n is a multiple of 3, otherwise 0.
13
1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1
OFFSET
0
FORMULA
a(n) = [A003415(n) == 0 (mod 3)], where [ ] is the Iverson bracket.
From Antti Karttunen, Jun 13 2024: (Start)
a(n) = A267142(n) + A369658(n) = A267142(n) + A011655(n)*A373371(n).
For n > 0, a(n) = [n == 0 (mod 9)] + [n != 0 (mod 3)]*[A373591(n) == A373592(n) (mod 3)].
a(n) = [0 == A373253(n)] = 1 - (A373254(n) + A373256(n)).
a(n) >= A369643(n).
a(n) >= A373143(n).
a(n) >= A370118(n).
(End)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359430(n) = !(A003415(n)%3);
(PARI) A359430(n) = if(!n, 1, if(!(n%3), !(n%9), 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==((m1-m2)%3))); \\ Antti Karttunen, Jun 13 2024
CROSSREFS
Characteristic function of A327863.
Cf. also A369643, A369653 [= a(A276086(n))], A370118, A370122 [= a(A003415(n))], A373143.
Sequence in context: A279484 A279329 A374117 * A374121 A292438 A244525
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 02 2023
STATUS
approved