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 A215896 Largest k = 2^(m - 1)*(2^m - 1) such that bigomega(k) = n or 0 if no such k exists. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 A261868 A342922 Adjacent sequences: A215893 A215894 A215895 * A215897 A215898 A215899 KEYWORD nonn AUTHOR Gerasimov Sergey, Aug 25 2012. STATUS approved

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Last modified June 15 13:08 EDT 2024. Contains 373407 sequences. (Running on oeis4.)