

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
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OFFSET

2,2


COMMENTS

Or, smallest b such that 1/n + 1/c = 1/b has integer solutions.
Largest b is (n1) since 1/n + 1/(n(n1)) = 1/(n1).
a(n) = smallest k such that k*n/(kn) 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) a(n)={my(k=1); if(n>1, while (n*k%(n + k), k++); n*k/(n + k))} \\ 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. AdamsWatters, Aug 07 2009


STATUS

approved



