A173695 Numbers k such that lambda(k) = lambda(k+1).

1, 3, 15, 90, 104, 495, 665, 702, 740, 836, 975, 1628, 2625, 2834, 2849, 3800, 7384, 12402, 12560, 13050, 15250, 16470, 22935, 25928, 26274, 29574, 29890, 32864, 39524, 41451, 44286, 47519, 48326, 48704, 48872, 49050, 50850, 53130, 54816, 56790, 56864, 57584, 63456

Offset: 1

Author

Michel Lagneau, Nov 25 2010

Keywords

• nonn

Comments

Lambda(n) is the Carmichael lambda function (A002322).

For k>3 in the sequence, k and k+1 are both composite. - Robert Israel, Oct 31 2016

Numbers k such that lambda(k) = lambda(k+1) = lambda(k+2) are 16274635445, 42107181364, and no more below 1.6*10^11. - Amiram Eldar, May 30 2023

Examples

			104 is in the sequence because lambda(104) = lambda(105) = 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..372 from Robert Israel)

Crossrefs

Cf. A002322.

Programs

Maple

with(numtheory):for n from 1 to 50000 do:if lambda(n)=lambda(n+1)then printf(`%d,
  `, n):else fi:od:

Mathematica

seq[kmax_] := Module[{s = {}, c1 = 0, c2}, Do[c2 = CarmichaelLambda[k]; If[c1 == c2, AppendTo[s, k - 1]]; c1 = c2, {k, 1, kmax}]; s]; seq[10^5] (* Amiram Eldar, Feb 22 2023 *)
SequencePosition[CarmichaelLambda[Range[64000]],{x_,x_}][[;;,1]] (* Harvey P. Dale, Feb 22 2023 *)

PARI

lista(kmax) = {my(c1 = 0, c2); for(k = 1, kmax, c2 = lcm(znstar(k)[2]); if(c1 == c2, print1(k-1,", ")); c1 = c2);} \\ Amiram Eldar, Feb 22 2023