A106051 Number of divisors of the Euler number E(2n) (A000364).

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, 32, 128, 4, 192, 32, 64, 32, 64, 8, 512, 32, 32, 4, 96, 16, 64, 16, 64, 8, 64, 16, 2048, 32, 64, 8, 32, 32, 512, 32, 1024, 64, 32, 16, 96, 16, 512, 256, 2048, 8, 32

Offset: 0

Author

John W. Layman, May 06 2005

Keywords

• nonn

Comments

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,...}.

Examples

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..86

Crossrefs

Cf. A000005, A000364.

Programs

Maple

a:= n-> numtheory[tau](abs(euler(2*n))):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 03 2023

Mathematica

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

Formula

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

Extensions

a(34)-a(49) from Robert G. Wilson v, May 09 2005

a(46) corrected and more terms from Sean A. Irvine, Mar 03 2023