A340092 Carmichael numbers k for which A053575(k) [the odd part of phi] does not divide k-1.

1729, 2821, 15841, 29341, 41041, 52633, 63973, 75361, 101101, 115921, 126217, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 488881, 512461, 530881, 552721, 656601, 658801, 670033, 748657, 825265, 838201, 852841, 997633, 1024651, 1033669, 1050985, 1082809, 1152271, 1193221, 1461241, 1569457

Offset: 1

Author

Antti Karttunen, Dec 31 2020

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Complement of A339869 in A002997.

Subsequence of A340091.

Cf. A002322, A053575.

Programs

Mathematica

odd[n_] := n/2^IntegerExponent[n, 2]; Select[Range[1, 10^6, 2], CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] && !Divisible[# - 1, odd @ EulerPhi[#]] &] (* Amiram Eldar, Dec 31 2020 *)

PARI

A000265(n) = (n>>valuation(n, 2));
A002322(n) = lcm(znstar(n)[2]);
isA340092(n) = ((n>1)&&!isprime(n)&&(!((n-1)%A002322(n)))&&(0<((n-1)%A000265(eulerphi(n)))));