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A260406 Numbers n such that (n-1)^2-1 divides 2^(n-1)-1.

%I A260406 #22 Sep 08 2022 08:46:13
%S A260406 1,3,5,17,37,257,457,1297,2557,4357,6481,8009,11953,26321,44101,47521,
%T A260406 47881,49681,57241,65537,74449,84421,97813,141157,157081,165601,
%U A260406 225457,278497,310591,333433,365941,403901,419711,476737,557041,560737,576721,647089,1011961
%N A260406 Numbers n such that (n-1)^2-1 divides 2^(n-1)-1.
%C A260406 The initial 1 is conventional.
%C A260406 647089 is the smallest composite number of this sequence (which makes it different from A081762).
%C A260406 The next composite number in this sequence is a(1000) = F_5 = 4294967297. - _Robert G. Wilson v_, Jul 25 2015
%C A260406 The Fermat numbers 2^2^k+1 = A000215(k) with k>1 are a subsequence of this sequence. I conjecture that they are equal to the intersection of this and A260407 (apart from the conventional 1), i.e., the numbers such that (n-1)^4-1 divides 2^(n-1)-1.
%H A260406 Robert G. Wilson v, <a href="/A260406/b260406.txt">Table of n, a(n) for n = 1..1598</a>
%t A260406 fQ[n_] := PowerMod[2, n - 1, (n - 1)^2 - 1] == 1; Select[ Range[3, 1200000], fQ] (* _Robert G. Wilson v_, Jul 25 2015 *)
%o A260406 (PARI) forstep(n=1,1e7,2,Mod(2,(n-1)^2-1)^(n-1)==1&&print1(n","))
%o A260406 (Magma) [n: n in [3..6*10^5] | (2^(n-1)-1) mod ((n-1)^2-1) eq 0]; // _Vincenzo Librandi_, Jul 26 2015
%Y A260406 Cf. A081762, A260072, A260407.
%K A260406 nonn
%O A260406 1,2
%A A260406 _M. F. Hasler_, Jul 24 2015