A186309 - OEIS

%I #16 May 19 2014 15:21:54

%S 36,540,39852,75418035,113570688,120668856,141963360,150836070,

%T 18826510275,37653020550,106746035772831,213492071545662,

%U 2906980416141000,4360470624211500,11118121391391372

%N Numbers n having more than one representation as k*(1+phi(k)/2), where phi(k) is Euler's totient function.

%C The computations were provided by _Robert Israel_ from sci.math.  He found no n that had three representations up to k < 10^6.  It would be a challenge to find an n with three representations.

%H Math Forum, <a href="http://mathforum.org/kb/message.jspa?messageID=7370315&amp;tstart=0">Topic: a(1+ phi(a)/2) = b(1+phi(b)/2) </a>

%e For 36, sum of the coprimes of 9 is 27, add to 9 to get 36; the sum of the coprimes of 12 is 24, add 12  to 24 to also get 36.  The corresponding {a,b} for each term is listed at the sci.math reference.

%K nonn

%O 1,1

%A _J. M. Bergot_, Feb 17 2011

%E a(11)-a(15) from _Donovan Johnson_, Feb 21 2011