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- W2074663398 abstract "If r, k are positive integers, then Tkr(n) denotes the number of k-tuples of positive integers (x1, x2, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r = 1. An explicit formula for Tkr(n) is derived and it is shown that limn→∞Tkr(n)nk = 1ζ(rk). If S = {p1, p2, …, pa} is a finite set of primes, then 〈S〉 = {p1a1p2a2…psas; pi ∈ S and ai ≥ 0 for all i} and Tkr(S, n) denotes the number of k-tuples (x1, x3, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r ∈ 〈S〉. Asymptotic formulas for Tkr(S, n) are derived and it is shown that limn→∞Tkr(S, n)nk = (p1 … pa)rkζ(rk)(p1rk − 1) … (psrk − 1)." @default.
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- W2074663398 date "1976-05-01" @default.
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- W2074663398 title "The probability that k positive integers are relatively r-prime" @default.
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- W2074663398 doi "https://doi.org/10.1016/0022-314x(76)90103-7" @default.
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