A162464 Numbers n which are concatenations n=x//y such that x^2+y^3 is a multiple of n.

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

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^(j-1) then next fi;
    x:= (n-y)/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