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(2*n-1)-perfect numbers.
4

%I #15 Mar 13 2014 02:41:56

%S 20,128768,33501184

%N (2*n-1)-perfect numbers.

%C For the definition see A175837.

%C Considering only terms of the form 2^k * p with p prime results in a linear equation for p for a given k. Solving quickly generates other terms of the sequence: 137433972736, 2199001235456, 649037107316852462774394019643392, and a 157-digit term associated with k=260. - _D. S. McNeil_, Dec 08 2010

%F A033880(a(n))=A000005(a(n))/2-1.

%e Proper divisors of 20 are: 1,2,4,5,10. Since 2*20-1=(2*1-1)+(2*2-1)+(2*4-1)+(2*5-1)+(2*10-1)=39, then 20 is in the sequence.

%Y Cf. A175837 (abundant version), A175522, A033880, A000005.

%K nonn,hard,more,bref

%O 1,1

%A _Vladimir Shevelev_, Dec 05 2010

%E a(3) from _D. S. McNeil_, Dec 08 2010