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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
OFFSET
1,1
COMMENTS
From Thomas Ordowski, Sep 12 2017: (Start)
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
a(17) > 1206. - Amiram Eldar, Apr 01 2021
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^n-1)); if (sum(k=1, #f~, ((f[k, 1]-1) % n)==0) == 1, print1(n, ", ")));
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Michel Marcus, Sep 12 2017
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