A337316 Composite numbers k such that phi(k) divides d*(k - 1) for some squarefree divisor d of k - 1.

1729, 12801, 247105, 1224721, 2704801, 5079361, 8355841, 26906881, 30240001, 34479361, 36426241, 45318561, 48188161, 49871361, 61485601, 107714881, 170947105, 178312321, 193708801, 393760321, 446569201, 475683841, 740376001, 781347841, 878169601, 987275521, 1022304361

Offset: 1

Author

Tomohiro Yamada, Sep 28 2020

Keywords

• nonn

Comments

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.

Examples

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

Links

• Max Alekseyev, Table of n, a(n) for n = 1..114

Crossrefs

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

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

Programs

Mathematica

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

PARI

is(n)={my(s=denominator((n-1)/eulerphi(n))); !isprime(n) && issquarefree(s) && ((n-1)%s==0) && n>1}
{ forcomposite(n=1, 2^28, if(is(n), print1(n, ", "))) }

Extensions

More terms from Amiram Eldar, Oct 14 2020