A063428 a(n) is the smallest positive integer of the form n*k/(n+k).

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

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.

Mathematica

spi[n_]:=Module[{k=1}, While[!IntegerQ[(n*k)/(n+k)], k++]; (n*k)/(n+k)]; Array[ spi, 80, 2] (* Harvey P. Dale, May 05 2022 *)

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. Adams-Watters, Aug 07 2009

Status

approved