cp's OEIS Frontend

A061645 a(n) is the number of divisors of n-th even perfect number.

%I A061645 #61 Oct 18 2024 11:42:21
%S A061645 4,6,10,14,26,34,38,62,122,178,214,254,1042,1214,2558,4406,4562,6434,
%T A061645 8506,8846,19378,19882,22426,39874,43402,46418,88994,172486,221006,
%U A061645 264098,432182,1513678,1718866,2515574,2796538,5952442,6042754,13945186,26933834
%N A061645 a(n) is the number of divisors of n-th even perfect number.
%C A061645 The number of divisors of n-th perfect number that are powers of 2 is equal to a(n)/2, assuming there are no odd perfect numbers. The number of divisors of n-th perfect number that are multiples of n-th Mersenne prime A000668(n) is also equal to a(n)/2, assuming there are no odd perfect numbers. (See A000043). - _Omar E. Pol_, Feb 28 2008
%C A061645 The n-th even perfect number A000396(n) = 2^(p-1)*P with Mersenne prime P = 2^p-1, p = A000043(n), has obviously the 2p divisors { 1, 2, 2^2, ..., 2^(p-1) } U { P, 2*P, ..., 2^(p-1)*P }. - _M. F. Hasler_, Dec 10 2018
%H A061645 Amiram Eldar, <a href="/A061645/b061645.txt">Table of n, a(n) for n = 1..48</a> (terms 1..47 from Ivan Panchenko)
%H A061645 Omar E. Pol, <a href="http://www.polprimos.com/#Los%20n%C3%BAmeros%20perfectos">Los números perfectos</a>, (in Spanish).
%F A061645 a(n) = A000005(A000396(n)).
%F A061645 a(n) = floor{log_2(A000396(n))} + 2. - _Lekraj Beedassy_, Aug 21 2004
%F A061645 a(n) = 2*A000043(n). - _M. F. Hasler_, Dec 05 2018
%e A061645 8128 = 2*2*2*2*2*2*127 with 14 divisors.
%t A061645 2 * Array[MersennePrimeExponent, 45] (* _Amiram Eldar_, Dec 10 2018 *)
%o A061645 (PARI) A061645(n)=2*A000043(n) \\ with A000043(n)=[...][n], the dots being replaced by DATA from A000043. - _M. F. Hasler_, Dec 05 2018
%Y A061645 Cf. A000005, A000043, A000396, A000668.
%K A061645 nonn
%O A061645 1,1
%A A061645 _Labos Elemer_, Jun 14 2001
%E A061645 Definition changed (inserting the word "even") by _Ivan Panchenko_, Apr 16 2018
%E A061645 a(38)-a(39) from _Ivan Panchenko_, Apr 16 2018