A∩P2 Sample Clauses

A∩P2. To do so, we introduce a weight function w(n) and instead sum w(a). Let λ be a real number such that 2 ≤ λ < 3, and assume x is sufficiently large so that G(n) ≤ xλ for all n ≤ x. If n is a positive integer, let pn and ω(n) denote the smallest prime divisor of n and the number of distinct prime divisors of n, respectively. For a prime p < xλ/2 such that p|n, let  1 − log p if p = pn ωp(n) :=  then let λ/2 log x log pn  1 − λ/2 log x log p λ/2 log x if p > pn and p < xλ/4 if p > pn and p ≥ xλ/4, w(n) := 1 − 3 − λ p|n,Σp<xλ/2 ωp(n). (3.2) Remark. The weights w(n) are the same weights that Xxxxxxx used, which are due to Xxxxxxx (unpublished, see [44]). Xxxxxxx [53] developed weights which would yield a slightly better implied constant for the asymptotic #(A∩P2) log x x , but since we have suppressed the constant, we choose to use Xxxxxxx’x weights to maintain continuity with Xxxxxxx. We require a lemma due to Xxxxxxx [00, Xxxxx 1], which asserts that the weight function w(n) detects P2 for squarefree n.
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A∩P2. 1. The adjectives can have subsective interpretations not available in predicative position.10

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