

A106051


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


0



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, 16, 16, 2048, 32, 64
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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

Table of n, a(n) for n=0..50.


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. 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


STATUS

approved



