A292079 Composite numbers m such that 2^m - 1 has a single prime factor of the form k*m + 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

Links

Table of n, a(n) for n=1..16.

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

Cf. A001265, A002326, A182590.

Sequence in context: A115684 A373879 A020201 * A161760 A213308 A067127

Adjacent sequences: A292076 A292077 A292078 * A292080 A292081 A292082

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