

A162464


Numbers n which are concatenations n=x//y such that x^2+y^3 is a multiple of n.


1



43, 48, 63, 101, 111, 117, 143, 159, 189, 284, 402, 459, 464, 903, 1068, 1575, 1604, 2212, 2505, 3468, 3606, 3672, 4587, 4907, 6408, 7812, 8109, 11211, 11817, 12129, 12336, 12663, 12987, 14443, 15873, 19089, 20274, 22557, 23177, 33759, 40900, 41579, 61075, 65628
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OFFSET

1,1


COMMENTS

Concatenations with x=0 or y=0 or that allow y with leading zeros are not taken into account.


LINKS

Robert Israel, Table of n, a(n) for n = 1..250


EXAMPLE

43 is in the list because 4^2+3^3 = 16+27= 43 = 1x43.
159 is in the list because 15^2+9^3 = 225+729 = 954 = 6x159.
11211 is in the list because 1^2+1211^3 = 158412*11211.
10001 is not in the list although 100^2+(01)^3 = 1*10001, because it requires a leading zero in y.


MAPLE

filter:= proc(n) local j, x, y;
for j from 1 to ilog10(n) do
y:= n mod 10^j;
if y < 10^(j1) then next fi;
x:= (ny)/10^j;
if ((x^2+y^3)/n)::integer then return true fi
od:
false
end proc:
select(filter, [$1..10^5]); # Robert Israel, May 22 2016


CROSSREFS

Sequence in context: A180519 A118485 A165444 * A255224 A161406 A128653
Adjacent sequences: A162461 A162462 A162463 * A162465 A162466 A162467


KEYWORD

nonn,base


AUTHOR

Claudio Meller, Jul 04 2009


EXTENSIONS

Missing terms inserted by R. J. Mathar, Jul 10 2009


STATUS

approved



