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A273202 Minimal terms of A274720.

%I A273202 #35 May 09 2021 02:16:26
%S A273202 9,21,25,39,49,55,57,111,121,155,169,183,201,203,205,219,237,253,289,
%T A273202 291,301,305,309,327,355,361,417,453,489,497,505,529,543,579,597,633,
%U A273202 655,689,723,737,755,791,813,841,889,905,921,939,955,961,979,993,1011
%N A273202 Minimal terms of A274720.
%C A273202 Terms m of A274720 such that no nontrivial divisor of m is in A274720.
%C A273202 The terms consist of the following:
%C A273202 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).
%C A273202 p*q where p < q are odd primes and p divides the order of 2 mod q.
%H A273202 Robert Israel, <a href="/A273202/b273202.txt">Table of n, a(n) for n = 1..10000</a>
%e A273202 39 is a term because it is in A274720 and its nontrivial divisors 3 and 13 are not in A274720.
%p A273202 N:= 10000: # less than 1093^2 so we don't need to worry about powers of
%p A273202            # Wieferich primes
%p A273202 Primes:= select(isprime, [seq(i,i=3..N/3)]):
%p A273202 S:= {}:
%p A273202 for q in Primes do
%p A273202   m:= numtheory:-order(2,q);
%p A273202   ps:= numtheory:-factorset(m) union {q} minus {2};
%p A273202   S:= S union select(`<=`,map(`*`,ps,q),N)
%p A273202 od:
%p A273202 sort(convert(S,list));
%t A273202 A274720 = Select[Range[1, 2000, 2], !CoprimeQ[MultiplicativeOrder[2, #], #]&]; Select[A274720, NoneTrue[Divisors[#][[2;;-2]], MemberQ[A274720, #]&]&] (* _Jean-François Alcover_, Apr 27 2019 *)
%Y A273202 Cf. A001220, A002326, A274720.
%K A273202 nonn
%O A273202 1,1
%A A273202 _Robert Israel_, Jul 27 2016