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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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified May 7 12:56 EDT 2021. Contains 343650 sequences. (Running on oeis4.)