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A173572
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Odd integers n such that 2^n == 4 (mod n).
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16
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1, 20737, 93527, 228727, 373457, 540857, 2231327, 11232137, 15088847, 15235703, 24601943, 43092527, 49891487, 66171767, 71429177, 137134727, 207426737, 209402327, 269165561, 302357057, 383696711, 513013327
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OFFSET
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1,2
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COMMENTS
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Also, nonprime integers n such that 2^(n-2) == 1 (mod n).
For all m, 2^A050259(m)-1 belongs to this sequence.
If n > 1 is a term and p is a primitive prime factor of 2^(n-2)-1, then n*p is also a term. Hence, the sequence is infinite. (Rotkiewicz 1984)
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REFERENCES
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A. E. Bojarincev, Asymptotic expressions for the n-th composite number, Univ. Mat. Zap. 6:21-43 (1967). (in Russian)
R. K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, Third Edition, 2004
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
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LINKS
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MAPLE
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with(numtheory): for n from 1 to 100000000 do: a:= 2^(n-2)- 1; b:= a / n; c:= floor(b): if b = c and tau(n) <> 2 then print (n); else fi; od:
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MATHEMATICA
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m = 4; Join[Select[Range[1, m, 2], Divisible[2^# - m, #] &], Select[Range[m + 1, 10^6, 2], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 12 2018 *)
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PROG
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(PARI) is(n) = n%2==1 && Mod(2, n)^n==Mod(4, n) \\ Jinyuan Wang, Feb 22 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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