A106051 - OEIS

%I #13 Mar 03 2023 17:54:14

%S 1,1,2,2,4,4,16,4,8,8,12,8,16,4,128,4,32,8,64,2,48,8,64,8,16,16,128,

%T 32,128,4,192,32,64,32,64,8,512,32,32,4,96,16,64,16,64,8,64,16,2048,

%U 32,64,8,32,32,512,32,1024,64,32,16,96,16,512,256,2048,8,32

%N Number of divisors of the Euler number E(2n) (A000364).

%C Notice that all listed terms are powers of 2 except for the 10th, 20th and 30th. It would be interesting to know whether this pattern continues. Note: Various sources give differing values for the Euler numbers. A000364 gives {1,1,5,61,1385,50521,2702765,199360981,19391512145,...}, whereas Mathematica gives {1,0,-1,0,5,0,-61,0,1385,0,-50521,...}.

%H Sean A. Irvine, <a href="/A106051/b106051.txt">Table of n, a(n) for n = 0..86</a>

%F a(n) = A000005(A000364(n)).

%e E(4) = 1385 has divisors {1,5,277,1385}, so a(4) = 4.

%p a:= n-> numtheory[tau](abs(euler(2*n))):

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 03 2023

%t a ={};For[n=0, n<=33, n++, {Eu=EulerE[2*n];L=Length[Divisors[Eu]];a=Append[a, L]}];a

%Y Cf. A000005, A000364.

%K nonn

%O 0,3

%A _John W. Layman_, May 06 2005

%E a(34)-a(49) from _Robert G. Wilson v_, May 09 2005

%E a(46) corrected and more terms from _Sean A. Irvine_, Mar 03 2023