This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A292364 #20 Jan 10 2019 23:07:46
%S A292364 4,8,9,12,24,121
%N A292364 Composites m such that each prime factor p > m of 2^m - 1 is a primitive prime factor of 2^m - 1.
%C A292364 From A086251: "A prime factor of 2^n-1 is called primitive if it does not divide 2^r-1 for any r<n. Equivalently, p is a primitive prime factor of 2^n-1 if ord(2,p)=n."
%C A292364 Are there only finitely many such composite numbers?
%C A292364 From _Charlie Neder_, Jan 09 2019: (Start)
%C A292364 Equivalently, composite numbers n such that, for each proper divisor d of n, 2^d-1 is n-smooth.
%C A292364 Let S represent the set of numbers such that the greatest prime factor of 2^n-1 is less than n^2. S begins {2,3,4,6,8,9,10,11,12,14,15,18,20,21,24,28,30,36,48,60} (obtained from A005420), and I conjecture that there are no further terms.
%C A292364 For any composite number k, if k has a divisor d >= sqrt(k) that is not in this sequence, then gpf(2^d-1) > d^2 >= k and k is not in this sequence.
%C A292364 If S is complete, there are 15 possible choices of k, the largest of which is 121, and this sequence is complete. (End)
%F A292364 A002326((p-1)/2) = m for every prime factor p > m of 2^m - 1.
%o A292364 (PARI) lista(nn) = {forcomposite (m=1, nn, f = factor(2^m-1)[,1]~; ok = 1; for (k=1, #f, p = f[k]; if ((p > m) && (znorder(Mod(2, p)) != m), ok = 0; break);); if (ok, print1(m, ", ")););} \\ _Michel Marcus_, Nov 11 2017
%Y A292364 Cf. A002326, A060443, A086251.
%K A292364 nonn,more
%O A292364 1,1
%A A292364 _Thomas Ordowski_, Sep 15 2017