A276980 Odd squarefree numbers n > 1 such that lambda(n)^2 = phi(n), where lambda is the Carmichael lambda function and phi is Euler's totient function.

273, 1729, 2109, 2255, 4433, 4641, 4697, 5673, 6643, 6935, 7667, 8103, 8729, 10235, 11543, 14497, 16385, 16523, 17507, 18915, 20033, 22649, 23579, 26691, 29309, 29393, 34799, 35853, 35929, 37209, 37829, 39277, 42653, 45551, 55699, 56163, 68735, 68901, 69167, 69977, 70993, 73505, 75361, 76373

Offset: 1

Author

Thomas Ordowski and Altug Alkan, Apr 11 2017

Keywords

• nonn

Comments

Such a number n must have at least three prime factors.

Are there infinitely many such numbers?

Among them are some Carmichael numbers: 1729, 75361, ... (A002997).

Examples

			273 = 3 * 7 * 13, so phi(273) = 2 * 6 * 12 = 144 = 12^2 and lambda(273) = lcm(2, 6, 12) = 12, hence 273 is in the sequence.
Notice that phi(315) = 144 and lambda(315) = 12 also. However, mu(315) = 0 since 315 = 3^2 * 5 * 7, so for that reason 315 is not in the sequence.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1024

Crossrefs

Subsequence of A024556.

Cf. A000010, A002322, A002997.

Programs

Mathematica

samePsiSqPhiQ[n_] := SquareFreeQ[n] && CarmichaelLambda[n]^2 == EulerPhi[n]; Select[1 + 2 Range@50000, samePsiSqPhiQ] (* Robert G. Wilson v, Apr 14 2017 *)

PARI

is(n) = n>1 && n%2!=0 && issquarefree(n) && lcm(znstar(n)[2])^2==eulerphi(n) \\ Felix Fröhlich, Apr 22 2017