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

Author

T. D. Noe, Nov 05 2007

Keywords

• nonn

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.

Examples

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

Links

• Achim Flammenkamp, The Multiply Perfect Numbers Page

Crossrefs

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