A339818 Carmichael numbers k for which the 2-adic valuation of phi(k) does not exceed the 2-adic valuation of k-1.

1729, 15841, 3057601, 3828001, 5310721, 8355841, 8830801, 9439201, 14676481, 15829633, 17236801, 40280065, 78091201, 83099521, 84350561, 92625121, 94536001, 104852881, 118901521, 129762001, 157731841, 163954561, 180115489, 193708801, 214852609, 221884001, 279377281, 382304161, 382536001, 438359041, 481239361, 511338241

Offset: 1

Author

Antti Karttunen, Dec 20 2020

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..22784 (terms below 2^64)

Crossrefs

Intersection of A002997 and A339817 (see comments in latter).

Cf. also A339869, A339878, A339909.

Programs

Mathematica

carmichaels = Cases[Import["https://oeis.org/A002997/b002997.txt", "Table"], {, }][[;; , 2]]; q[n_] := IntegerExponent[EulerPhi[n], 2] <= IntegerExponent[n - 1, 2]; Select[carmichaels, q] (* Amiram Eldar, Dec 26 2020 *)

PARI

A002322(n) = lcm(znstar(n)[2]); \\ From A002322
isA339818(n) = ((n>1)&&issquarefree(n)&&!isprime(n)&&(valuation(eulerphi(n),2)<=valuation(n-1,2))&&(0==((n-1)%A002322(n))));