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%I #42 Apr 01 2021 09:43:53
%S 4,6,8,9,12,20,24,27,33,49,69,77,145,425,447,567
%N Composite numbers m such that 2^m - 1 has a single prime factor of the form k*m + 1.
%C From _Thomas Ordowski_, Sep 12 2017: (Start)
%C Composite numbers m such that A182590(m) = 1.
%C Problem: are there infinitely many such numbers?
%C 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)
%C After 567, the only numbers < 1200 that may possibly be terms are 961, 1037, 1111, and 1115. - _Jon E. Schoenfield_, Dec 03 2017
%C a(17) > 1206. - _Amiram Eldar_, Apr 01 2021
%t 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 *)
%o (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, ", ")));
%Y Cf. A001265, A002326, A182590.
%K nonn,more
%O 1,1
%A _Michel Marcus_, Sep 12 2017
%E Erroneous terms 841 and 1127 and possible (but unconfirmed, and not necessarily next) term 1037 deleted by _Jon E. Schoenfield_, Dec 03 2017
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