A063649 - OEIS

%I #15 Jun 07 2020 17:57:07

%S 3,4,6,6,10,8,12,12,15,12,21,14,21,24,24,18,30,20,36,30,33,24,42,30,

%T 39,36,44,30,55,32,48,44,51,60,63,38,57,52,72,42,78,44,66,72,69,48,84,

%U 56,75,68,78,54,90,80,105,76,87,60,110,62,93,112,96,90,110,68,102,92,120

%N Largest b such that 1/n=1/c+1/b has integer solutions with c>b.

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

%H Robert Israel, <a href="/A063649/b063649.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = n*A063648(n)/(A063648(n)-n) = 2n-A063428(n).

%F From _Robert Israel_, Dec 01 2019: (Start)

%F a(n) = n + A063717(n).

%F a(n) = n + 1 if and only if n is prime. (End)

%e a(10)=15 since 1/10=1/20+1/20=1/30+1/15=1/35+1/14=1/60+1/12=1/110+1/11, but the first sum does not have c>b, leaving the second sum to provide the value.

%p f:= proc(n) local b;

%p   for b from 2*n-1 by -1 do

%p      if n*b mod (b-n) = 0 then return b fi

%p od

%p end proc:

%p map(f, [$2..100]); # _Robert Israel_, Dec 01 2019

%t a[n_] := n + SelectFirst[Divisors[n^2] // Reverse, #<n&];

%t a /@ Range[2, 100] (* _Jean-François Alcover_, Jun 07 2020 *)

%Y Cf. A018892, A063427, A063428, A063647, A063648.

%K nonn,look

%O 2,1

%A _Henry Bottomley_, Jul 23 2001