login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A063428 a(n) is the smallest positive integer of the form n*k/(n+k). 9
1, 2, 2, 4, 2, 6, 4, 6, 5, 10, 3, 12, 7, 6, 8, 16, 6, 18, 4, 12, 11, 22, 6, 20, 13, 18, 12, 28, 5, 30, 16, 22, 17, 10, 9, 36, 19, 26, 8, 40, 6, 42, 22, 18, 23, 46, 12, 42, 25, 34, 26, 52, 18, 30, 7, 38, 29, 58, 10, 60, 31, 14, 32, 40, 22, 66, 34, 46, 20, 70, 8, 72, 37, 30, 38, 28, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Or, smallest b such that 1/n+1/c=1/b has integer solutions.

Largest b is (n-1) since 1/n+1/(n(n-1))=1/(n-1).

a(n) = smallest k such that k*n/(k-n) is an integer. - Derek Orr, May 29 2014

LINKS

Harry J. Smith, Table of n, a(n) for n=2,...,1000

FORMULA

a(n) = n*A063427(n)/(n+A063427(n)) =2n-A063649(n)

If n is prime a(n)=n-1. - Benoit Cloitre, Dec 31 2001

EXAMPLE

a(6) = 2 because 6*3/(6+3)=2 is the smallest integer of the form 6*k/(6+k).

a(10) = 5 since 1/10+1/10 = 1/5, 1/10+1/15 = 1/6, 1/10+1/40 = 1/8, 1/10+1/90 = 1/9 and so the first sum provides the value.

PROG

(PARI) { for (n=2, 1000, k=1; while (n*k%(n + k), k++); write("b063428.txt", n, " ", n*k/(n + k)) ) } [From Harry J. Smith, Aug 20 2009]

CROSSREFS

Cf. A018892, A063427, A127730, A063647, A063648, A063649, A066092.

Sequence in context: A122645 A122646 A028496 * A133439 A234649 A072300

Adjacent sequences:  A063425 A063426 A063427 * A063429 A063430 A063431

KEYWORD

nonn

AUTHOR

Henry Bottomley, Jul 19 2001

EXTENSIONS

New description from Benoit Cloitre, Dec 31 2001

Entry revised by N. J. A. Sloane, Feb 13 2007

Definition revised by Franklin T. Adams-Watters, Aug 07 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified January 22 22:38 EST 2018. Contains 298093 sequences.