Abstract
American Journal of Mathematics, vol. xxii., No. 4.—Asymptotic evaluation of certain totient sums, by D. N. Lehmer, is an attempt to account for what seems to be a remarkable law, first observed in particular cases in 1895. It is thus stated: Consider any set s of k linear forms, an + bi(i=1 … k), all of which have the same modulus a, and where [a, bi]=1, [a, b] stands for the G.C. divisor of a and b. Consider, further, a function θ3,(x) such that θ3,(x) = 1 or 0, according as each of the prime divisors of x belongs to one of the forms of the set s or not. If, then, υ(x) denotes the number of distinct primes in x, we have
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Scientific Serials . Nature 63, 218 (1900). https://doi.org/10.1038/063218a0
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DOI: https://doi.org/10.1038/063218a0