A316906 Numbers k such that 2^(k-1) == 1 (mod k) and lpf(k)-1 does not divide k-1.

7957, 23377, 30889, 35333, 42799, 49981, 60787, 91001, 129889, 150851, 162193, 164737, 241001, 249841, 253241, 256999, 280601, 318361, 387731, 452051, 481573, 556169, 580337, 617093, 665333, 722201, 838861, 877099, 1016801, 1251949, 1252697, 1325843, 1507963

Offset: 1

Author

Thomas Ordowski, Jul 16 2018

Keywords

• nonn

Comments

Are there infinitely many such pseudoprimes?

Examples

			7957 = 73*109 is pseudoprime and 72 does not divide 7956.
30889 = 17*23*79 is pseudoprime and 16 does not divide 30888.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A001567.

Cf. A020639 (lpf(n)).

Programs

Mathematica

Select[Range[760000] 2 + 1, PowerMod[2, #-1, #] == 1 && Mod[#-1, FactorInteger[#][[1, 1]] - 1] > 0 &] (* Giovanni Resta, Jul 16 2018 *)

Extensions

a(8)-a(33) from Giovanni Resta, Jul 16 2018