A215896 Largest k = 2^(m - 1)*(2^m - 1) such that bigomega(k) = n or 0 if no such k exists.

1, 0, 6, 28, 0, 496, 0, 8128, 2016, 0, 130816, 0, 2096128, 33550336, 0, 0, 134209536, 8589869056, 0, 137438691328, 0, 0, 0, 34359607296, 35184367894528, 8796090925056, 0, 562949936644096, 2251799780130816, 9007199187632128, 140737479966720, 2305843008139952128, 0

Offset

1,3

Comments

Largest k = 2^(m-1)*(2^m-1) such that bigomega(k) = prime(n) or 0 if no such k exists (other version): 6, 28, 496, 8128, 0, 0, 8589869056, 137438691328, 34359607296, 9007199187632128, 2305843008139952128, 0, ...

Mersenne exponents (A000043): numbers n such that omega(2^(n-1)*(2^n-1)) = 2, or bigomega(2^(n-1)*(2^n-1)) = n, or tau(2^(n-1)*(2^n-1)) = 2n, or sigma(2^(n-1)*(2^n-1)) = 2^n*(2^n-1).

Smallest k = 2^(m-1)*(2^m-1) such that bigomega(k) = n or 0 if no such k exists : 1, 0, 6, 28, 0, 120, 0, 8128, 2016, 0, 32640, 0, 523776, 33550336, 0, 0, 8386560, 536854528, 0, 2147450880, 0, 0, 0, 34359607296, 2199022206976, 549755289600, 0, 562949936644096, 2251799780130816,...

Links

Table of n, a(n) for n=1..33.

Example

a(0) = 1 because 2^(1-1)*(2^1-1) = 1 and A001222(1) = 0,
a(2) = 6 because 2^(2-1)*(2^2-1) = 6 and A001222(6) = 2,
a(3) = 28 because 2^(3-1)*(2^3-1) = 28 and A001222(28) = 3,
a(5) = 496 because 2^(4-1)*(2^4-1) = 120, 2^(5-1)*(2^5-1) = 496 and A001222(120) = A001222(496) = 5, 496 > 120.
a(7) = 8128 because 2^(7-1)*(2^7-1) = 8128 and A001222(8128) = 7,
a(8) = 2016 because 2^(6-1)*(2^6-1) = 2016 and A001222(2016) = 8,
a(10) = 130816 because 2^(8-1)*(2^8-1) = 32640, 2^(9-1)*(2^9-1) = 130816 and A001222(32640) = A001222(130816) = 10, 130816 > 32640.

Maple

A215896 := proc(n)
      local m, k;
      for m from n+2 by -1 do
        k := 2^(m-1)*(2^m-1) ;
        if k < 0 then
            return 0 ;
        end if;
        if numtheory[bigomega](k) = n then
            return k ;
        end if;
    end do:
end proc: # R. J. Mathar, Sep 11 2012

Crossrefs

Cf. A000396, A006516, A046051, A144858.

Sequence in context: A064810 A101454 A091911 * A211679 A379500 A261868

Adjacent sequences: A215893 A215894 A215895 * A215897 A215898 A215899

Keyword

nonn

Author

Gerasimov Sergey, Aug 25 2012.

Status

approved