OFFSET
1,1
COMMENTS
The terms consist of the following:
p^(b+1) where p is an odd prime and b is the largest exponent k such that p^k divides 2^(p-1)-1 (in particular b=1 if p is not a Wieferich prime).
p*q where p < q are odd primes and p divides the order of 2 mod q.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
MAPLE
N:= 10000: # less than 1093^2 so we don't need to worry about powers of
# Wieferich primes
Primes:= select(isprime, [seq(i, i=3..N/3)]):
S:= {}:
for q in Primes do
m:= numtheory:-order(2, q);
ps:= numtheory:-factorset(m) union {q} minus {2};
S:= S union select(`<=`, map(`*`, ps, q), N)
od:
sort(convert(S, list));
MATHEMATICA
A274720 = Select[Range[1, 2000, 2], !CoprimeQ[MultiplicativeOrder[2, #], #]&]; Select[A274720, NoneTrue[Divisors[#][[2;; -2]], MemberQ[A274720, #]&]&] (* Jean-François Alcover, Apr 27 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Jul 27 2016
STATUS
approved