

A230166


Terms of A222263 such that 2n/sigma(n)  1 = 1/2^k, for some integer k.


1



1, 3, 15, 135, 819, 1365, 1485, 2295, 9009, 13923, 63855, 387387, 397575, 667275, 14381055, 16410735, 99558459, 271543725, 3145425129, 7096702977, 741585912975, 2148325363107, 4847048133291, 39206559148911, 53164445037705, 130468907286855, 1229923663366167
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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 = 21 = 1 = 1/2^0 is of the required form with k=0.
For n=2, 2*2/sigma(2)1 = 4/31 = 1/3 is not of the form 1/2^k.
a(2)=3 since 2*3/sigma(3)1 = 6/41 = 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

Cf. A222263.
Sequence in context: A006717 A222263 A246804 * A059861 A232699 A030539
Adjacent sequences: A230163 A230164 A230165 * A230167 A230168 A230169


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



