

A181711


Numbers of the form m*(2^k1), where m = 2^(k1)*(2^k1) is a perfect number (A000396).


0




OFFSET

1,1


COMMENTS

The associated exponents k are in A000043: 2, 3, 5, 7, 13, 17, 19 ,31, 61, ...
One can prove that, if m = 2^(k1)*(2^k1) is a perfect number, then m*2^k and m*(2^k1) are both in A181595. Thus every even term in A000396 is a difference of two terms in A181595.


LINKS

Table of n, a(n) for n=1..9.


FORMULA

If odd perfect numbers do not exist, then a(n) = A181710(n)  A000396(n).
a(n) = A019279(n)*(A000668(n))^2 if there are no odd superperfect numbers.  César Aguilera, Jun 13 2017


EXAMPLE

With k=3, m = 2^(k1)*(2^k  1) = 2^2*(8  1) = 28 is a perfect number (A000396), so m*(2^k  1) = 28*7 = 196 is in the sequence.  Michael B. Porter, Jul 19 2016


CROSSREFS

Cf. A000043, A000396, A181595, A181596, A181701, A181710.
Sequence in context: A125406 A318161 A182311 * A042940 A264356 A034727
Adjacent sequences: A181708 A181709 A181710 * A181712 A181713 A181714


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Nov 07 2010


EXTENSIONS

Definition condensed by R. J. Mathar, Dec 05 2010


STATUS

approved



