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A246503 Numbers m such that m^2 divides 2^k - 1 for some k, 0 < k <= m.

%I A246503 #35 Jan 09 2025 18:38:03
%S A246503 1,1093,3279,3511,5465,7651,9837,10533,14209,16395,17555,18581,22953,
%T A246503 24577,31599,31697,38255,38621,42627,45643,46999,49185,52665,53557,
%U A246503 55743,57929,60115,62301,66709,68859,71045,73731,84161,86347,92905,94797,95091,99463
%N A246503 Numbers m such that m^2 divides 2^k - 1 for some k, 0 < k <= m.
%C A246503 All terms are odd. m=1 is the only term with k=m.
%C A246503 Odd numbers m such that A007733(m^2) = A002326((m^2-1)/2) <= m.
%C A246503 Prime terms are Wieferich primes (A001220).
%H A246503 Chai Wah Wu, <a href="/A246503/b246503.txt">Table of n, a(n) for n = 1..127</a>
%o A246503 (Python)
%o A246503 A246503_list = [1]
%o A246503 for i in range(2, 10**4):
%o A246503     d, n = i*i, 1
%o A246503     for _ in range(i):
%o A246503         n = (2*n) % d
%o A246503         if n == 1:
%o A246503             A246503_list.append(i)
%o A246503             break # _Chai Wah Wu_, Dec 04 2014
%Y A246503 Cf. A001220, A002326.
%K A246503 nonn
%O A246503 1,2
%A A246503 _Max Alekseyev_, Nov 29 2014