A276733 - OEIS

%I #17 Sep 30 2016 13:27:09

%S 341,1247,1387,2047,2701,3277,3683,4033,4369,4681,5461,5963,7957,8321,

%T 9017,9211,10261,13747,14351,14491,15709,17593,18721,19951,20191,

%U 23377,24929,25351,29041,31417,31609,31621,33227,35333,37901,42799,45761,46513,49141,49601,49981

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

%C Super-Poulet numbers A050217 is a subsequence.

%C From _Robert Israel_, Sep 16 2016: (Start)

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

%C 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)

%H Robert Israel, <a href="/A276733/b276733.txt">Table of n, a(n) for n = 1..1000</a>

%p filter:= n -> not isprime(n) and 2 &^ min(numtheory:-factorset(n)) - 2 mod n = 0:

%p select(filter, [seq(i,i=3..100000,2)]); # _Robert Israel_, Sep 16 2016

%o (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

%Y Cf. A006530, A020639, A050217.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Sep 16 2016

%E More terms from _Michel Marcus_, Sep 16 2016