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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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 9 20:04 EDT 2024. Contains 375044 sequences. (Running on oeis4.)