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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)