cp's OEIS Frontend

A133033 Number of proper divisors of n-th even perfect number.

%I A133033 #28 Oct 18 2024 11:42:07
%S A133033 3,5,9,13,25,33,37,61,121,177,213,253,1041,1213,2557,4405,4561,6433,
%T A133033 8505,8845,19377,19881,22425,39873,43401,46417,88993,172485,221005,
%U A133033 264097,432181,1513677,1718865,2515573,2796537,5952441,6042753,13945185,26933833,41992021,48073165,51929901,60804913
%N A133033 Number of proper divisors of n-th even perfect number.
%C A133033 Perfect numbers: A000396(n) = 2^a(n) - 2^A090748(n), assuming there are no odd perfect numbers.
%C A133033 Also, a(n) is equal to the number of bits in A135650(n), the n-th even perfect number written in base 2.
%C A133033 These are odd numbers k such that 2^((k+1)/2) - 1 is (a Mersenne) prime. - _Thomas Ordowski_, Apr 20 2019
%H A133033 Amiram Eldar, <a href="/A133033/b133033.txt">Table of n, a(n) for n = 1..48</a> (terms 1..47 from Ivan Panchenko)
%H A133033 Chris K. Caldwell, "Top Twenty" page, <a href="https://t5k.org/top20/page.php?id=4">Mersenne Primes</a>.
%H A133033 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%F A133033 a(n) = A061645(n) - 1.
%F A133033 a(n) = A000043(n) + A090748(n) = 2*A000043(n) - 1 = 2*A090748(n) + 1.
%t A133033 2 * MersennePrimeExponent[Range[48]] - 1 (* _Amiram Eldar_, Oct 18 2024 *)
%Y A133033 Cf. A000043, A000396, A061645, A090748, A135650.
%K A133033 nonn
%O A133033 1,1
%A A133033 _Omar E. Pol_, Oct 27 2007, Feb 23 2008, Apr 28 2009
%E A133033 a(39)-a(43) from _Ivan Panchenko_, Apr 12 2018