

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.


1



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
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OFFSET

1,1


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).


LINKS

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


EXAMPLE

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.


MATHEMATICA

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


PROG

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


CROSSREFS

Subsequence of A024556.
Cf. A000010, A002322, A002997.
Sequence in context: A043467 A028530 A200836 * A214220 A029567 A028534
Adjacent sequences: A276977 A276978 A276979 * A276981 A276982 A276983


KEYWORD

nonn


AUTHOR

Thomas Ordowski and Altug Alkan, Apr 11 2017


STATUS

approved



