A276733 Composite numbers n such that 2^lpf(n) == 2 (mod n), where lpf(n) = A020639(n).

341, 1247, 1387, 2047, 2701, 3277, 3683, 4033, 4369, 4681, 5461, 5963, 7957, 8321, 9017, 9211, 10261, 13747, 14351, 14491, 15709, 17593, 18721, 19951, 20191, 23377, 24929, 25351, 29041, 31417, 31609, 31621, 33227, 35333, 37901, 42799, 45761, 46513, 49141, 49601, 49981

Offset: 1

Author

Thomas Ordowski, Sep 16 2016

Keywords

• nonn

Comments

Super-Poulet numbers A050217 is a subsequence.

From Robert Israel, Sep 16 2016: (Start)

If p is a Wieferich prime (A001220), p^2 is in this sequence.

If p is a non-Wieferich prime, there are terms of the sequence divisible by p iff p < A006530(2^p-2). Is the latter true for all primes p except 2,3,5,7 and 13? (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006530, A020639, A050217.

Programs

Maple

filter:= n -> not isprime(n) and 2 &^ min(numtheory:-factorset(n)) - 2 mod n = 0:
select(filter, [seq(i,i=3..100000,2)]); # Robert Israel, Sep 16 2016

PARI

lista(nn) = forcomposite(n=2, nn, if (Mod(2, n)^factor(n)[1,1] == Mod(2, n), print1(n, ", "));); \\ Michel Marcus, Sep 16 2016

Extensions

More terms from Michel Marcus, Sep 16 2016