A162464 - OEIS

%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