Abstract
Lehmer's totient problem asks if there exist composite integers n satisfying the condition φ(n)|(n - 1) (where φ is the Euler-phi function), while Carmichael numbers satisfy the weaker condition λ(n)|(n - 1) (where λ is the Carmichael universal exponent function). We weaken the condition further, looking at those composite n where each prime divisor of φ(n) also divides n - 1. ( So rad (φ(n))|(n - 1).) While these numbers appear to be far more numerous than the Carmichael numbers, we show that their distribution has the same rough upper bound as that of the Carmichael numbers, a bound which is heuristically tight.
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