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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.
3
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?
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.
Sequence in context: A030213 A187969 A132151 * A238469 A288596 A284745
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 21 2024
STATUS
approved