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A359828
Characteristic function for primitive elements of A235992.
4
1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1
OFFSET
1
COMMENTS
a(n) = 1 if A003415(n), the arithmetic derivative of n, is even, but for all divisors d|n, 1<d<n, A358680(d)*A358680(n/d) = 0. Otherwise a(n) = 0.
FORMULA
a(n) = A358680(n) * [0 == Sum_{d|n, 1<d<n} A358680(d)*A358680(n/d)], where [ ] is the Iverson bracket.
PROG
(PARI)
A358680(n) = if(n<=1, 1, my(f=factor(n)); 0==((n*sum(i=1, #f~, f[i, 2]/f[i, 1]))%2));
A359828(n) = if(!A358680(n), 0, fordiv(n, d, if((d>1)&&(d<n)&&A358680(d)&&A358680(n/d), return(0))); (1));
CROSSREFS
Characteristic function of A359829.
Sequence in context: A373374 A120523 A269625 * A359781 A030315 A119498
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 17 2023
STATUS
approved