

A292079


Composite numbers m such that 2^m  1 has a single prime factor of the form k*m + 1.


1



4, 6, 8, 9, 12, 20, 24, 27, 33, 49, 69, 77, 145, 425, 447, 567
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OFFSET

1,1


COMMENTS

Composite numbers m such that A182590(m) = 1.
Problem: are there infinitely many such numbers?
Note that this single prime factor p is the only primitive prime factor of 2^m  1 for all such m except 6, i.e., the multiplicative order of 2 modulo p is m. (End)
After 567, the only numbers < 1200 that may possibly be terms are 961, 1037, 1111, and 1115.  Jon E. Schoenfield, Dec 03 2017


LINKS



MATHEMATICA

Select[Range@ 150, And[CompositeQ@ #, Function[{m, p}, Total@ Boole@ Map[Divisible[#  1, m] &, p] == 1] @@ {#, FactorInteger[2^#  1][[All, 1]]}] &] (* Michael De Vlieger, Dec 06 2017 *)


PROG

(PARI) lista(nn) = forcomposite(n=1, nn, my(f = factor(2^n1)); if (sum(k=1, #f~, ((f[k, 1]1) % n)==0) == 1, print1(n, ", ")));


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS

Erroneous terms 841 and 1127 and possible (but unconfirmed, and not necessarily next) term 1037 deleted by Jon E. Schoenfield, Dec 03 2017


STATUS

approved



