A134666 Number of multiply perfect numbers (A007691) having 2^n as the highest power of 2.

1, 1, 2, 2, 1, 4, 1, 5, 4, 4, 3, 6, 1, 3, 4, 5, 1, 9, 1, 19, 8, 9, 3, 5, 6, 7, 16, 13, 26, 20, 1, 6, 8, 6, 13, 23, 20, 6, 9, 33, 10, 11, 14, 18, 15, 13, 32, 23, 23, 18, 12, 20, 26, 21, 16, 17, 7, 11, 20, 15, 1, 10, 17, 14, 13, 26, 21, 16, 24, 13, 21, 27, 18, 14, 16, 21, 38, 19, 12, 26, 13, 23

Offset

0,3

Comments

It appears that a(n)>0 for all n. With the exception of n=2, a(n)=1 when n is p-1, where p is a Mersenne prime (A000043). Flammenkamp has an attractive graph of this sequence, including n for which there is incomplete data.

Links

Table of n, a(n) for n=0..81.

Achim Flammenkamp, The Multiply Perfect Numbers Page

Example

a(2)=2 because only 28 and 2178540 have 2^2 as their highest power of 2.

Crossrefs

Cf. A134665 (highest power of 2 for each MPN).

Sequence in context: A174714 A116633 A263232 * A129712 A051720 A022693

Adjacent sequences: A134663 A134664 A134665 * A134667 A134668 A134669

Keyword

nonn

Author

T. D. Noe, Nov 05 2007

Status

approved