A330446 Composite numbers k such that 2^(k-1) == - lambda(k) (mod k), where lambda is the Carmichael lambda function (A002322).

140, 1054, 1068, 4844, 11209, 19856, 24949, 28390, 78184, 423796, 769516, 4283544, 5935168, 13116053, 122189752, 441252296, 528500308, 636697392, 669629030, 669778082, 1228748591

Offset: 1

Author

Amiram Eldar and Thomas Ordowski, Dec 15 2019

Keywords

• nonn
• more

Comments

Composite numbers k such that A062173(k) = A277127(k).

The odd terms are 11209, 24949, 13116053, ...

Note that if p is an odd prime, then 2^(p-1) == - lambda(p) (mod p), because lambda(p) = p-1.

Examples

			140 is a term since it is composite and 2^(140-1) == 140 - lambda(140) == 128 (mod 140).
		

Crossrefs

Cf. A002322, A062173, A277127.

Programs

Mathematica

Select[Range[10^6], CompositeQ[#] && PowerMod[2, # - 1, #] == # - CarmichaelLambda[#] &]