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A049479
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Smallest prime dividing 2^n - 1.
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18
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3, 7, 3, 31, 3, 127, 3, 7, 3, 23, 3, 8191, 3, 7, 3, 131071, 3, 524287, 3, 7, 3, 47, 3, 31, 3, 7, 3, 233, 3, 2147483647, 3, 7, 3, 31, 3, 223, 3, 7, 3, 13367, 3, 431, 3, 7, 3, 2351, 3, 127, 3, 7, 3, 6361, 3, 23, 3, 7, 3, 179951, 3, 2305843009213693951, 3, 7, 3, 31
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OFFSET
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2,1
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COMMENTS
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If p is prime then a(p) == 1 (mod p). Are there composite numbers k such that a(k) == 1 (mod k)? - Thomas Ordowski, Jan 27 2014
Yes, up to 1200, the following composites have the desired property: 169, 221, 323, 611, 779, 793, 923, 1121, 1159. - Michel Marcus, Jan 28 2014
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LINKS
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FORMULA
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a(n) > lpf(n) while a(2k) = 3 and a(2k+1) > 2*lpf(2k+1), where lpf(m) = A020639(m). - Thomas Ordowski, Jan 29 2014
For k >= 1, a(2k) = 3, a(6k-3)=7. - Zak Seidov, Mar 21 2014
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EXAMPLE
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a(6)=3 since 2^6 - 1 = 63 = 3^2*7.
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MATHEMATICA
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a = {}; Do[w = 2^n - 1; c = FactorInteger[w]; b = c[[1]][[1]]; AppendTo[a, b], {n, 2, 65}]; a (* Artur Jasinski, Dec 11 2007 *)
FactorInteger[#][[1, 1]]&/@(2^Range[2, 70]-1) (* Harvey P. Dale, Nov 18 2019 *)
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PROG
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(Python)
from sympy import factorint
return min(factorint(2**n-1)) # Chai Wah Wu, Jun 03 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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More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
Terms to a(500) in b-file from T. D. Noe, Dec 06 2006
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STATUS
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approved
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