A273202 Minimal terms of A274720.

9, 21, 25, 39, 49, 55, 57, 111, 121, 155, 169, 183, 201, 203, 205, 219, 237, 253, 289, 291, 301, 305, 309, 327, 355, 361, 417, 453, 489, 497, 505, 529, 543, 579, 597, 633, 655, 689, 723, 737, 755, 791, 813, 841, 889, 905, 921, 939, 955, 961, 979, 993, 1011

Offset

1,1

Comments

Terms m of A274720 such that no nontrivial divisor of m is in A274720.

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

39 is a term because it is in A274720 and its nontrivial divisors 3 and 13 are not in A274720.

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

Cf. A001220, A002326, A274720.

Sequence in context: A340482 A324722 A295230 * A338909 A173456 A192192

Adjacent sequences: A273199 A273200 A273201 * A273203 A273204 A273205

Keyword

nonn

Author

Robert Israel, Jul 27 2016

Status

approved