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A110082 Numbers of the form 2^(m-1)*(4^m+2^m-1) where 4^m+2^m-1 is prime. 2
5, 38, 284, 2168, 133088, 537394688, 140739635806208, 2361183382172302573568, 151115729703628426969088, 20282409604241966234288777068544, 45671926166590726335069952848216804538059849728 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
LINKS
F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1
EXAMPLE
2^1299*(4^1300+2^1300-1) is in the sequence because 4^1300+2^1300-1 is prime.
MATHEMATICA
Do[If[PrimeQ[4^m+2^m-1], Print[2^(m-1)*(4^m+2^m-1)]], {m, 52}]
CROSSREFS
Sequence in context: A279489 A027323 A110079 * A073508 A282964 A357163
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Aug 03 2005
STATUS
approved

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Last modified April 17 21:01 EDT 2024. Contains 371767 sequences. (Running on oeis4.)