A370124 a(0) = 0, a(1) = 1, and for n > 1, a(n) = 1 if the least prime dividing the arithmetic derivative of n is equal to the least prime not dividing n, otherwise a(n) = 0.

0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1

Offset

0

Comments

Question: Does this sequence have an asymptotic mean?

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Formula

For n > 1, a(n) = [A020639(A003415(n)) == A053669(n)], where [ ] is the Iverson bracket.

For n > 1, a(n) = [A020639(A003415(n)) == A020639(A276086(n))].

Example

a(1) = 1 because A003415(1) = 0, every prime divides zero, including the smallest of primes, which is 2, and 2 is also the least prime that does not divide 1.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
A053669(n) = forprime(p=2, , if(n%p, return(p)));
A370124(n) = if(n<2, n, (A020639(A003415(n))==A053669(n)));

Crossrefs

Characteristic function of A370125.

Cf. A003415, A020639, A053669, A276086.

Sequence in context: A030213 A187969 A132151 * A238469 A288596 A284745

Adjacent sequences: A370121 A370122 A370123 * A370125 A370126 A370127

Keyword

nonn

Author

Antti Karttunen, Feb 21 2024

Status

approved