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%I #4 Mar 30 2012 17:37:43
%S 168,2976,48768,201302016,51539214336,824632147968,
%T 13835058048839712768,15950735949418990467928155695723053056,
%U 1149371655649416643768760268505821828785983929289015296
%N Numbers of the form 3*2^p*(2^p-1) where 2^p-1 is a (Mersenne) prime greater than 3.
%C If n is in the sequence then sigma(n) = 4*(n-phi(n)) because phi(n) = phi(3)*phi(2^p)*phi(2^p-1) = 2^p*(2^p-2) hence 4*(n-phi(n)) = 4*(3*2^p*(2^p-1)-2^p*(2^p-2)) = 4*2^p* (3*2^p-3-2^p+2) = 4*2^p*(2^(p+1)-1) = sigma(3)*sigma(2^p-1)* sigma(2^p) = sigma(3*(2^p-1)*2^p) = sigma(n). So this sequence is a subsequence of A068420.
%t Do[If[PrimeQ[2^Prime[n] - 1], Print[3*2^Prime[n]* (2^Prime[n] - 1)]], {n, 2, 28}]
%Y Cf. A000668, A068420.
%K nonn
%O 1,1
%A _Farideh Firoozbakht_, Jul 27 2005; definition corrected Apr 22 2006
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