A110082 Numbers of the form 2^(m-1)*(4^m+2^m-1) where 4^m+2^m-1 is prime.

5, 38, 284, 2168, 133088, 537394688, 140739635806208, 2361183382172302573568, 151115729703628426969088, 20282409604241966234288777068544, 45671926166590726335069952848216804538059849728

Offset: 1

Author

Farideh Firoozbakht, Aug 03 2005

Keywords

• nonn

Comments

This sequence is a subsequence of A110079 namely, if n is in the sequence then sigma(n)=2n-2^d(n) where d(n) is number of positive divisors of n(see comments line of the sequence A110079). Sequence A110080 gives numbers n such that 4^n+2^n-1 is prime.

Examples

			2^1299*(4^1300+2^1300-1) is in the sequence because 4^1300+2^1300-1 is prime.
		

Links

• F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1

Crossrefs

Cf. A110079, A098855.

Programs

Mathematica

Do[If[PrimeQ[4^m+2^m-1], Print[2^(m-1)*(4^m+2^m-1)]], {m, 52}]