A274720 -id:A274720 - cp's OEIS frontend

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

Robert Israel, Jul 27 2016

nonn

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.

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

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001220, A002326, A274720.

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));

A274720 = Select[Range[1, 2000, 2], !CoprimeQ[MultiplicativeOrder[2, #], #]&]; Select[A274720, NoneTrue[Divisors[#][[2;;-2]], MemberQ[A274720, #]&]&] (* Jean-François Alcover, Apr 27 2019 *)

cp's OEIS Frontend

A273202 Minimal terms of A274720.

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