A146768 - OEIS

%I #67 Feb 24 2025 04:34:35

%S 1,2,3,6,8,9,15,30,44,53,63,260,303,639,1101,1140,1608,2126,2211,4844,

%T 4970,5606,9968,10850,11604,22248,43121,55251,66024,108045,378419,

%U 429716,628893,699134,1488110,1510688,3486296,6733458,10498005,12018291,12982475,15201228

%N a(n) is the number k such that 2^(2k+1)-1 = A000668(n+1).

%C The least common multiple of an even superperfect number greater than 2 and its arithmetic derivative divided by the number itself, i.e., lcm(A061652(i), A061652(i)')/A061652(i). - _Giorgio Balzarotti_, Apr 21 2011

%H Amiram Eldar, <a href="/A146768/b146768.txt">Table of n, a(n) for n = 1..46</a>

%H C. K. Caldwell, <a href="https://t5k.org/top20/page.php?id=4">Top 20 Mersenne primes</a>

%H Bernhard Helmes, <a href="http://devalco.de/quadr_Sieb_2x%5E2-1.php">Prime generator f(n)=2n^2-1</a>

%H George Woltman, <a href="http://www.mersenne.org/default.php">Great Internet Mersenne Prime Search</a>

%F a(n) = (A000043(n+1) - 1)/2.

%F 2^(2*a(n) + 1) - 1 = A000668(n+1). - _M. F. Hasler_, Jan 27 2020

%t (MersennePrimeExponent[Range[2, 47]] - 1)/2 (* _Amiram Eldar_, Mar 29 2020 *)

%Y Cf. A000043, A000668, A061652.

%K nonn,changed

%O 1,2

%A _Artur Jasinski_, Nov 02 2008

%E Term for the 39th Mersenne prime added by _Roderick MacPhee_, Oct 05 2009

%E Formula and edits from _Charles R Greathouse IV_, Aug 14 2010

%E Updated to include 40th Mersenne prime by _Michael B. Porter_, Nov 26 2010

%E a(40)-a(42) from _Amiram Eldar_, Mar 29 2020