A188466 Numbers n such that lambda(n) = lambda(n + lambda(n)).

1, 4, 6, 16, 36, 55, 78, 105, 124, 144, 171, 200, 253, 325, 406, 465, 666, 689, 715, 741, 915, 930, 990, 1027, 1081, 1136, 1240, 1421, 1448, 1610, 1653, 1711, 1752, 1764, 1800, 1827, 2211, 2352, 2448, 2667, 2800, 2835, 3403, 3600, 3619, 3620, 3660, 3900, 4840, 4970, 5253, 5264, 5513, 5671, 5886, 6100, 6328, 8001, 8112

Offset: 1

Author

Michel Lagneau, Apr 01 2011

Keywords

• nonn

Comments

Lambda is the function (A002322). If there are infinitely many Sophie Germain primes (conjecture), then this sequence is infinite. Proof: The numbers of the form p(2p+1) are in a subsequence if p and 2p+1 are both prime with p > 3, because from the property that lambda(p(2p+1)) = p(p-1), if m = p(2p+1) then lambda(m+phi(m)) = lambda (p(2p+1) + p(p-1)) = lambda(3p^2) = p(p-1) = lambda(m).

Examples

			36 is in the sequence because lambda(36) = 6, and lambda(36 + 6) = lambda(42) = 6.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002322, A005384.

Cf. A185165: Numbers n such that lambda(n)= lambda(n - lambda(n)).

Cf. A051487: Numbers n such that phi(n) = phi(n - phi(n)).

Cf. A108569: Numbers n such that phi(n) = phi(n + phi(n)).

Programs

Magma

[1] cat [n: n in [2..8140] | CarmichaelLambda(n) eq CarmichaelLambda(n+CarmichaelLambda(n))];  // Bruno Berselli, Apr 10 2011

Mathematica

Select[Range[20000], CarmichaelLambda[ #] == CarmichaelLambda[ # + CarmichaelLambda[#]  ] &]

PARI

lambda(n) = lcm(znstar(n)[2]);
isok(n) = lambda(n) == lambda(n+lambda(n)); \\ Michel Marcus, May 12 2018