A175853 (2*n-1)-perfect numbers.

20, 128768, 33501184

Offset

1,1

Comments

For the definition see A175837.

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

Links

Table of n, a(n) for n=1..3.

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A165344 A348646 A222745 * A340167 A013766 A078354

Adjacent sequences: A175850 A175851 A175852 * A175854 A175855 A175856

Keyword

nonn,hard,more,bref

Author

Vladimir Shevelev, Dec 05 2010

Extensions

a(3) from D. S. McNeil, Dec 08 2010

Status

approved