A264012 Composite numbers n such that gcd(phi(n), n-1) = lambda(n), where lambda(n) = A002322(n).

561, 1105, 2821, 6601, 10585, 29341, 52633, 62745, 63973, 101101, 115921, 126217, 188461, 252601, 278545, 294409, 410041, 512461, 552721, 748657, 825265, 1152271, 1193221, 2100901, 2508013, 2531845, 3146221, 4335241, 4767841, 4909177, 5444489, 5481451, 6049681

Offset: 1

Author

Thomas Ordowski, Nov 01 2015

Keywords

• nonn

Comments

Carmichael numbers n such that A049559(n) = A002322(n).

If n is a Carmichael number with n-1 squarefree, then n is in the sequence. The smallest such n = 139952671.

If (n-1)/lambda(n) is a prime (see A174590), then n is in the sequence. - Thomas Ordowski, Oct 17 2016

Numbers n such that gcd(phi(n),n-1) = lambda(n)^2 are 1, 2, 2320690177, ? - Thomas Ordowski and Michel Marcus, Oct 20 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002322, A002997, A049559, A257643.

Programs

Mathematica

Select[ Range@ 6100000, CompositeQ@# && GCD[ EulerPhi@#, # - 1] == CarmichaelLambda@# &] (* Michael De Vlieger, Nov 01 2015 *)

PARI

forcomposite(n=1, 1e7, if(gcd(eulerphi(n),n-1)==lcm(znstar(n)[2]), print1(n ", "))) \\ Altug Alkan, Nov 01 2015

PARI

t(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1;
is(n)=n%2 && !isprime(n) && t(n) && n>1;
c(n)=gcd(eulerphi(n),n-1)/lcm(znstar(n)[2]);
for(n=1, 1e7, if(is(n) && c(n)==1 , print1(n", "))) \\ Altug Alkan, Nov 01 2015

Extensions

More terms from Altug Alkan, Nov 01 2015