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

20, 128768, 33501184

Offset: 1

Author

Vladimir Shevelev, Dec 05 2010

Keywords

• nonn
• hard
• more
• bref

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

Examples

			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.

Formula

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

Extensions

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