A273202 - OEIS

%I #35 May 09 2021 02:16:26

%S 9,21,25,39,49,55,57,111,121,155,169,183,201,203,205,219,237,253,289,

%T 291,301,305,309,327,355,361,417,453,489,497,505,529,543,579,597,633,

%U 655,689,723,737,755,791,813,841,889,905,921,939,955,961,979,993,1011

%N Minimal terms of A274720.

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

%C The terms consist of the following:

%C 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 p*q where p < q are odd primes and p divides the order of 2 mod q.

%H Robert Israel, <a href="/A273202/b273202.txt">Table of n, a(n) for n = 1..10000</a>

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

%p N:= 10000: # less than 1093^2 so we don't need to worry about powers of

%p            # Wieferich primes

%p Primes:= select(isprime, [seq(i,i=3..N/3)]):

%p S:= {}:

%p for q in Primes do

%p   m:= numtheory:-order(2,q);

%p   ps:= numtheory:-factorset(m) union {q} minus {2};

%p   S:= S union select(`<=`,map(`*`,ps,q),N)

%p od:

%p sort(convert(S,list));

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

%Y Cf. A001220, A002326, A274720.

%K nonn

%O 1,1

%A _Robert Israel_, Jul 27 2016