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%I #7 May 23 2016 03:08:25
%S 43,48,63,101,111,117,143,159,189,284,402,459,464,903,1068,1575,1604,
%T 2212,2505,3468,3606,3672,4587,4907,6408,7812,8109,11211,11817,12129,
%U 12336,12663,12987,14443,15873,19089,20274,22557,23177,33759,40900,41579,61075,65628
%N Numbers n which are concatenations n=x//y such that x^2+y^3 is a multiple of n.
%C Concatenations with x=0 or y=0 or that allow y with leading zeros are not taken into account.
%H Robert Israel, <a href="/A162464/b162464.txt">Table of n, a(n) for n = 1..250</a>
%e 43 is in the list because 4^2+3^3 = 16+27= 43 = 1x43.
%e 159 is in the list because 15^2+9^3 = 225+729 = 954 = 6x159.
%e 11211 is in the list because 1^2+1211^3 = 158412*11211.
%e 10001 is not in the list although 100^2+(01)^3 = 1*10001, because it requires a leading zero in y.
%p filter:= proc(n) local j, x, y;
%p for j from 1 to ilog10(n) do
%p y:= n mod 10^j;
%p if y < 10^(j-1) then next fi;
%p x:= (n-y)/10^j;
%p if ((x^2+y^3)/n)::integer then return true fi
%p od:
%p false
%p end proc:
%p select(filter, [$1..10^5]); # _Robert Israel_, May 22 2016
%K nonn,base
%O 1,1
%A _Claudio Meller_, Jul 04 2009
%E Missing terms inserted by _R. J. Mathar_, Jul 10 2009
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