OFFSET
1,2
COMMENTS
For all n>1, sigma(n)>n, therefore 2n/sigma(n)-1 is always less than 1, i.e., k>0.
For k=1 to 11, the smallest known numbers to give 1/2^k are: 3, 15, 135, 2295, 1485, 1365, 63855, 16410735, 397575, 667275, 271543725.
For k=12 to 19, they are: unknown, 741585912975, unknown, 39206559148911, 2569480266942180207, 1712973775775070501, unknown, 299364435975778645966263.
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 1..39
EXAMPLE
a(1)=1 since 2*1/sigma(1)-1 = 2-1 = 1 = 1/2^0 is of the required form with k=0.
For n=2, 2*2/sigma(2)-1 = 4/3-1 = 1/3 is not of the form 1/2^k.
a(2)=3 since 2*3/sigma(3)-1 = 6/4-1 = 1/2 = 1/2^1 is of that form with k=1.
For a(3)=15, 2*15/sigma(15)-1 = 30/(1+3+5+15)-1 = 30/24 - 1 = 6/24 = 1/2^2 is of this form with k=2.
PROG
(PARI) is_A230166(n)=(n=2*n/sigma(n)-1)>>valuation(n, 2)==1 \\ - M. F. Hasler, Oct 12 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 11 2013
EXTENSIONS
a(21) from Donovan Johnson, Dec 28 2013
a(22)-a(27) from Hiroaki Yamanouchi, Sep 27 2014
STATUS
approved