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A181705
Numbers of the form 2^(t-1)*(2^t-9), where 2^t-9 is prime.
2
56, 368, 128768, 2087936, 8589344768, 2199013818368, 36893488108764397568, 904625697166532776746648320380374279912262923807289020860114158381451706368
OFFSET
1,1
COMMENTS
Subsequence of 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).)
MATHEMATICA
2^(#-1) (2^#-9)&/@Select[Range[3, 130], PrimeQ[2^#-9]&] (* Harvey P. Dale, Oct 24 2011 *)
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Nov 06 2010
EXTENSIONS
Edited by R. J. Mathar, Sep 12 2011
STATUS
approved