A291961 Numbers n > 1 such that 2^lambda(n) == 1 (mod n^2), where lambda(n) is the Carmichael lambda function (A002322).

1093, 3279, 3511, 7651, 10533, 14209, 17555, 22953, 31599, 42627, 45643, 52665, 99463, 136929, 157995, 228215, 298389, 410787, 684645, 2053935, 3837523, 11512569, 19187615, 26862661, 34537707, 49887799, 57562845, 80587983, 134313305, 149663397, 172688535, 241763949, 249438995, 349214593, 402939915, 448990191, 748316985, 1047643779, 1208819745, 1746072965, 2244950955, 3142931337, 5238218895

Offset: 1

Author

Amiram Eldar, Sep 06 2017

Keywords

• nonn

Comments

An alternative generalization of Wieferich primes (A001220).

A subsequence of A077816, since the A002322(n)|A000010(n). The first 12 terms are common.

15714656685 (see A265630) is also a term. - Michel Marcus, Sep 14 2017

Crossrefs

Cf. A265630, A001220, A002322, A077816, A182297, A246503.

Programs

Mathematica

Select[Range[2, 100000], Divisible[2^CarmichaelLambda[#] - 1, #^2] &]

PARI

isok(n) = Mod(2, n^2)^lcm(znstar(n)[2]) == 1; \\ Michel Marcus, Sep 11 2017

Extensions

a(32)-a(36) from Michel Marcus, Sep 11 2017

a(37)-a(41) from Michel Marcus, Sep 12 2017

a(42)-a(43) from Michel Marcus, Sep 14 2017