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 A181705 Numbers of the form 2^(t-1)*(2^t-9), where 2^t-9 is prime. 1
 56, 368, 128768, 2087936, 8589344768, 2199013818368, 36893488108764397568, 904625697166532776746648320380374279912262923807289020860114158381451706368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All entries are near-perfect numbers (A181595). (Proof: Let m=2^(t-1)*(2^t-9) be the entry. By the multiplicative property of the sigma-function, sigma(m)=(2^t-1)*(2^t-8). The abundance sigma(m)-2*m is therefore 8, and since all t involved are >=4, 8 is a divisor of m because 8 divides 2^(t-1).) LINKS MATHEMATICA 2^(#-1) (2^#-9)&/@Select[Range[3, 130], PrimeQ[2^#-9]&] (* Harvey P. Dale, Oct 24 2011 *) CROSSREFS Cf. A059610, A181595, A181701, A000396, A181703, A181704 Sequence in context: A003783 A088833 A181598 * A219826 A075283 A205313 Adjacent sequences:  A181702 A181703 A181704 * A181706 A181707 A181708 KEYWORD nonn AUTHOR Vladimir Shevelev, Nov 06 2010 EXTENSIONS Edited by R. J. Mathar, Sep 12 2011 STATUS approved

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Last modified April 20 10:12 EDT 2021. Contains 343130 sequences. (Running on oeis4.)