A359828 Characteristic function for primitive elements of A235992.

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.

Links

Table of n, a(n) for n=1..121.

Index entries for characteristic functions

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.

Cf. A003415, A235992, A358680, A359831.

Sequence in context: A373374 A120523 A269625 * A359781 A030315 A119498

Adjacent sequences: A359825 A359826 A359827 * A359829 A359830 A359831

Keyword

nonn

Author

Antti Karttunen, Jan 17 2023

Status

approved