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Numbers m such that m^2 divides 2^k - 1 for some k, 0 < k <= m.
3

%I #32 Jun 13 2021 03:23:28

%S 1,1093,3279,3511,5465,7651,9837,10533,14209,16395,17555,18581,22953,

%T 24577,31599,31697,38255,38621,42627,45643,46999,49185,52665,53557,

%U 55743,57929,60115,62301,66709,68859,71045,73731,84161,86347,92905,94797,95091,99463

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

%C All terms are odd. m=1 is the only term with k=m.

%C Odd numbers m such that A007733(m^2) = A002326((m^2-1)/2) <= m.

%C Prime terms are Wieferich primes (A001220).

%H Chai Wah Wu, <a href="/A246503/b246503.txt">Table of n, a(n) for n = 1..127</a>

%o (Python)

%o A246503_list = [1]

%o for i in range(2,10**4):

%o ....d, n = i*i, 1

%o ....for _ in range(i):

%o ........n = (2*n) % d

%o ........if n == 1:

%o ............A246503_list.append(i)

%o ............break # _Chai Wah Wu_, Dec 04 2014

%Y Cf. A001220, A002326.

%K nonn

%O 1,2

%A _Max Alekseyev_, Nov 29 2014