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A277366 Composite numbers k such that phi(k)*lambda(k) divides (k-1)^2, where phi(k) = A000010(k) and lambda(k) = A002322(k).

%I A277366 #41 Apr 24 2024 02:42:54
%S A277366 1729,670033,6840001,83099521,193708801,321197185,367804801,484662529,
%T A277366 1752710401,2320690177,5064928705,12820178449,32220147601,
%U A277366 257124585601,270177600001,301036080385,7043394657601,13237329899521,14276860416001,85661522006401,119377939968001
%N A277366 Composite numbers k such that phi(k)*lambda(k) divides (k-1)^2, where phi(k) = A000010(k) and lambda(k) = A002322(k).
%C A277366 Are there infinitely many such numbers?
%C A277366 Such k must be a Carmichael number since phi(k)*lambda(k) = m*lambda(k)^2 for some integer m. - _Nathan McNew_, Oct 11 2016
%H A277366 Amiram Eldar, <a href="/A277366/b277366.txt">Table of n, a(n) for n = 1..115</a> (terms below 10^22, calculated using data from Claude Goutier)
%H A277366 Claude Goutier, <a href="http://www-labs.iro.umontreal.ca/~goutier/OEIS/A055553/">Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22</a>.
%H A277366 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%t A277366 Select[Range[10^8], CompositeQ[#] && Divisible[(# - 1)^2, EulerPhi[#] * CarmichaelLambda[#]] &] (* _Amiram Eldar_, Feb 02 2019 *)
%o A277366 (PARI) lista(nn) = forcomposite(n=4, nn, if (((n-1)^2 % (eulerphi(n)*lcm(znstar(n)[2]))) == 0, print1(n, ", "));); \\ _Michel Marcus_, Oct 11 2016
%o A277366 (PARI) is(n,f=factor(n))=(n-1)^2%(eulerphi(f)*lcm(znstar(f)[2])) == 0 && !isprime(n) && n>1 \\ _Charles R Greathouse IV_, Oct 11 2016
%Y A277366 Subsequence of A002997 and of A173703.
%Y A277366 Cf. A000010, A002322, A002997, A173703.
%K A277366 nonn
%O A277366 1,1
%A A277366 _Thomas Ordowski_, Oct 11 2016
%E A277366 a(2)-a(3) from _Michel Marcus_, Oct 11 2016
%E A277366 a(4)-a(8) from _Charles R Greathouse IV_, Oct 11 2016
%E A277366 a(9)-a(13) from _David A. Corneth_, Oct 11 2016
%E A277366 More terms from _Amiram Eldar_, Feb 02 2019