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Composite numbers k such that phi(k) divides d*(k - 1) for some squarefree divisor d of k - 1.
2

%I #50 Sep 30 2023 09:43:38

%S 1729,12801,247105,1224721,2704801,5079361,8355841,26906881,30240001,

%T 34479361,36426241,45318561,48188161,49871361,61485601,107714881,

%U 170947105,178312321,193708801,393760321,446569201,475683841,740376001,781347841,878169601,987275521,1022304361

%N Composite numbers k such that phi(k) divides d*(k - 1) for some squarefree divisor d of k - 1.

%C All terms of this sequence are terms of A173703 (2-Lehmer numbers) and all Lehmer numbers (if there are any) are contained in this sequence.

%H Max Alekseyev, <a href="/A337316/b337316.txt">Table of n, a(n) for n = 1..114</a>

%e phi(247105) = 194688 divides 2 * 13 * 247104.

%t divQ[n_] := AnyTrue[Select[Divisors[n - 1], SquareFreeQ]*(n - 1), Divisible[#, EulerPhi[n]] &]; Select[Range[250000], CompositeQ[#] && divQ[#] &] (* _Amiram Eldar_, Oct 14 2020 *)

%o (PARI) is(n)={my(s=denominator((n-1)/eulerphi(n))); !isprime(n) && issquarefree(s) && ((n-1)%s==0) && n>1}

%o { forcomposite(n=1, 2^28, if(is(n), print1(n, ", "))) }

%Y Cf. A173703 (2-Lehmer numbers), A238574 (k-Lehmer numbers for some k).

%Y Cf. A000010 (phi), A005117 (squarefree numbers).

%K nonn

%O 1,1

%A _Tomohiro Yamada_, Sep 28 2020

%E More terms from _Amiram Eldar_, Oct 14 2020