A330446 - OEIS

A330446

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

%I #9 Dec 15 2019 08:36:40

%S 140,1054,1068,4844,11209,19856,24949,28390,78184,423796,769516,

%T 4283544,5935168,13116053,122189752,441252296,528500308,636697392,

%U 669629030,669778082,1228748591

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

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

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

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

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

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

%Y Cf. A002322, A062173, A277127.

%K nonn,more

%O 1,1

%A _Amiram Eldar_ and _Thomas Ordowski_, Dec 15 2019