cp's OEIS Frontend

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.

A247071 Numbers n such that 2^n-1 has only one primitive prime factor, sorted according to the magnitude of the corresponding prime.

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%I A247071 #40 Feb 12 2024 01:52:50
%S A247071 2,4,3,10,12,8,18,5,20,14,9,7,15,24,16,30,21,22,26,42,13,34,40,32,54,
%T A247071 17,38,27,19,33,46,56,90,78,62,31,80
%N A247071 Numbers n such that 2^n-1 has only one primitive prime factor, sorted according to the magnitude of the corresponding prime.
%C A247071 Periods associated with A144755 in base 2. The binary analog of A051627.
%F A247071 a(n) = A002326((A144755(n+1)-1)/2). - _Max Alekseyev_, Feb 11 2024
%e A247071 2^12 - 1 = 4095 = 3 * 3 * 5 * 7 * 13, but none of 3, 5, 7 is a primitive prime factor, so the only primitive prime factor of 2^12 - 1 is 13.
%t A247071 nmax = 65536; primesPeriods = Reap[Do[p = Cyclotomic[n, 2]/GCD[n, Cyclotomic[n, 2]]; If[PrimeQ[p], Print[n]; Sow[{p, n}]], {n, 1, nmax}]][[2, 1]]; Sort[primesPeriods][[All, 2]]
%Y A247071 Cf. A161508, A161509, A144755, A007498, A007615, A051627, A040017.
%K A247071 nonn,more
%O A247071 1,1
%A A247071 _Eric Chen_, Nov 16 2014
%E A247071 Sequence trimmed to the established terms of A144755 by _Max Alekseyev_, Feb 11 2024