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A338998
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Composite numbers k such that phi(k) divides p*(k - 1) for some prime factor p of k - 1.
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1
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OFFSET
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1,1
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COMMENTS
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All terms of this sequence are terms of A337316 and all Lehmer numbers (if there are any) are contained in this sequence.
Terms 1729 and 3069196417 and several others are also Carmichael numbers (A002997), they are given in A339878.
The sequence also includes: 1334063001601, 6767608320001, 33812972024833, 380655711289345, 1584348087168001, 1602991137369601, 6166793784729601, 1531757211193440001. - Daniel Suteu, Nov 24 2020
The "Lehmer numbers" above refers to composite 1-Lehmer numbers, that is, numbers n that would satisfy the equation y * phi(n) = n-1, for some integer y > 1. Lehmer conjectured that no such numbers exist. See the assorted Web-links. - Antti Karttunen, Dec 26 2020
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LINKS
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EXAMPLE
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phi(1729) = 1296 divides 3 * 1728.
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PROG
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(PARI) is(n)={my(s=denominator((n-1)/eulerphi(n))); !isprime(n) && isprime(s) && ((n-1)%s==0) && n>1}
{ forcomposite(n=1, 2^32, if(is(n), print1(n, ", "))) }
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CROSSREFS
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Subsequence of A173703 (2-Lehmer numbers).
Cf. A337316 (with "squarefree divisor" instead of "prime factor").
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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