%I A096823
%S A096823 6,20,12,151115727449904501489664,56,40,24,272,1504,208,176,1312,112,80,
%T A096823 48,6208,992,928,2059264,5696,736,144115176533131264,608,544,5056,416,
%U A096823 352,4672,224,160,96,24704,24448,3904,3776,487936,112384,3392,22912
%N A096823 Numbers of the form p*(p+(2n-1))/2 created with smallest primes of form 
               p=2^x-(2n-1)=A096522(n). Here the exponent equals x=A096502[n], the 
               least exponent providing this kind of primes. Peculiarity of the 
               present terms is as follows: Mod[sigma[a(n)],a[n]]=2*n.
%C A096823 These numbers are clearly analogous to perfect numbers.
%e A096823 a[1]=6 is the first even perfect number;
%e A096823 a[7]=24 corresponds to A096821(1)=24;
%e A096823 a[4]=151115727449904501489664=2^38*(2^39-7)=274877906944*549755813881;
%Y A096823 Cf. A096502, A096821, A096822.
%Y A096823 Sequence in context: A090590 A002566 A087998 this_sequence A007253 A096897 
               A063601
%Y A096823 Adjacent sequences: A096820 A096821 A096822 this_sequence A096824 A096825 
               A096826
%K A096823 nonn
%O A096823 1,1
%A A096823 Labos E. (labos(AT)ana.sote.hu), Jul 13 2004