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

2, 6, 8, 20, 42, 75, 90, 117, 154, 156, 189, 220, 363, 385, 490, 525, 702, 775, 777, 845, 975, 990, 1050, 1183, 1276, 1300, 1505, 1587, 1628, 1742, 1806, 1824, 1860, 1905, 1911, 2436, 2496, 2523, 2541, 2793, 2860, 2943, 3660, 3720, 3800, 3960, 4309, 5043, 5060, 5390, 5540, 5994, 6069, 6160, 6664, 6845, 8127, 8268, 8325, 8427

Offset: 1

Author

Michel Lagneau, Mar 31 2011

Keywords

• nonn

Comments

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

Examples

			75 is in the sequence because lambda(75) = 20, lambda(75 - 20) = lambda(55) = 20.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002322, A005384.

Cf. A051487 (numbers n such that phi(n) = phi(n - phi(n))).

Programs

Mathematica

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