OFFSET
1,1
COMMENTS
The eighteenth composite term is 3481. No other composite terms up to 10000.
LINKS
Dario Alejandro Alpern, Integer factorization calculator
John Brillhart et al., Cunningham Project [Factorizations of b^n +- 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers]
S. S. Wagstaff, Jr., The Cunningham Project
EXAMPLE
a(1) = 6 because 2^6 - 1 = 63 = 3^2*7 is a 3-almost prime.
a(2) = 8 because 2^8 - 1 = 255 = 3*5*17 is a 3-almost prime.
MATHEMATICA
ParallelMap[ If[ PrimeOmega[2^# - 1] == 3, #, Nothing] &, Range@1250] (* Robert G. Wilson v, Nov 28 2017 *)
PROG
(Magma) lst:=[]; factors:=func<n | Factorization(n)>; bigomega:=func<n | &+[d[2]: d in factors(n)]>; IsCube:=func<n | (n^(1/3)) eq Floor(n^(1/3))>; for n in [2..254] do if IsPrime(n) then if bigomega(2^n-1) eq 3 then Append(~lst, n); end if; else f:=factors(n); a:=f[1, 1]; if IsPrime(2^a-1) then if IsSquarefree(n) then if bigomega(n) eq 2 then b:=f[2, 1]; if IsPrime(2^b-1) and IsPrime(Truncate((2^n-1)/((2^a-1)*(2^b-1)))) then Append(~lst, n); end if; end if; end if; if IsSquare(n) or IsCube(n) then if bigomega(Truncate((2^n-1)/(2^a-1))) eq 2 then Append(~lst, n); end if; end if; end if; end if; end for; lst;
(PARI) is(n)=bigomega(2^n-1)==3
CROSSREFS
KEYWORD
nonn
AUTHOR
Arkadiusz Wesolowski, Nov 07 2017
EXTENSIONS
a(28)-a(56) added from the Cunningham project
STATUS
approved