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A105331
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Numbers of the form 2^n*(2^(n+1)+2n+1) where 2^(n+1)+2n+1 is prime.
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3
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3, 14, 52, 184, 656, 34688, 2118656, 134438912, 537346048, 9007202811510784, 2417851639318318791262208, 633825300114170432793740312576, 2535301200456572518883997515776
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OFFSET
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1,1
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COMMENTS
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This is because these numbers satisfy tau(n) + sigma(n) = 2n when n = 2^k * p with p is prime; for instance tau(14) + sigma(14) = 4 + 24 = 28 = 2 x 14. [See References.] - Bernard Schott, Apr 07 2017
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REFERENCES
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J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Ellipses, Problème 723, page 93.
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LINKS
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FORMULA
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EXAMPLE
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9007202811510784 is in the sequence because 9007202811510784 = 2^26*(2^27 + 2*26 + 1) and 2^27 + 2*26 + 1 is prime.
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MATHEMATICA
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Do[If[PrimeQ[2^(m + 1) + 2m + 1], Print[2^m(2^(m + 1) + 2m + 1)]], {m, 0, 110}]
2^# (2^(#+1)+2#+1)&/@Select[Range[0, 100], PrimeQ[2^(#+1)+2#+1]&] (* Harvey P. Dale, Nov 13 2012 *)
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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STATUS
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approved
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