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A359430
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a(n) = 1 if the arithmetic derivative of n is a multiple of 3, otherwise 0.
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13
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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
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OFFSET
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0
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LINKS
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FORMULA
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a(n) = [A003415(n) == 0 (mod 3)], where [ ] is the Iverson bracket.
For n > 0, a(n) = [n == 0 (mod 9)] + [n != 0 (mod 3)]*[A373591(n) == A373592(n) (mod 3)].
(End)
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PROG
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(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
(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
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CROSSREFS
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Characteristic function of A327863.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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