%I #22 May 05 2022 12:22:51

%S 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,

%T 5,30,16,22,17,10,9,36,19,26,8,40,6,42,22,18,23,46,12,42,25,34,26,52,

%U 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

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

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

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

%C a(n) = smallest k such that k*n/(k-n) is an integer. - _Derek Orr_, May 29 2014

%H Harry J. Smith, <a href="/A063428/b063428.txt">Table of n, a(n) for n = 2..1000</a>

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

%F If n is prime a(n) = n - 1. - _Benoit Cloitre_, Dec 31 2001

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

%e 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.

%t 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 *)

%o (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

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

%K nonn

%O 2,2

%A _Henry Bottomley_, Jul 19 2001

%E New description from _Benoit Cloitre_, Dec 31 2001

%E Entry revised by _N. J. A. Sloane_, Feb 13 2007

%E Definition revised by _Franklin T. Adams-Watters_, Aug 07 2009