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

0,3

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,...}.

Links

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

Formula

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

Example

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

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

Crossrefs

Cf. A000005, A000364.

Sequence in context: A321514 A280306 A140723 * A066781 A112869 A086117

Adjacent sequences: A106048 A106049 A106050 * A106052 A106053 A106054

Keyword

nonn

Author

John W. Layman, May 06 2005

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

Status

approved