A321881 Numbers whose sum and product of digits are cubes.

0, 1, 8, 10, 80, 100, 107, 170, 206, 260, 305, 350, 404, 440, 503, 530, 602, 620, 701, 710, 800, 999, 1000, 1007, 1016, 1025, 1034, 1043, 1052, 1061, 1070, 1106, 1124, 1142, 1160, 1205, 1214, 1241, 1250, 1304, 1340, 1403, 1412, 1421, 1430, 1502, 1520, 1601, 1610, 1700

Offset

1,3

Comments

The first numbers in the sequence that are cubes themselves are 0,1,8,1000,8000.

a(22)=999 is the only term up to n=120 related to the cube 27 (the previous ones relate to 0,1,8).

Also, a(22)=999 is the first term that has more than one digit and consists of a single repeated digit; the next ones are 11111111 and 333333333.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

93111111111111111 (15 ones) is in the sequence since the sum and the product of the digits is 27 (a cube).
333 is not in the sequence since the product of the digits is 27 but the sum is 9 (not a cube).

Maple

filter:= proc(n) local L;
  L:= convert(n, base, 10);
  simplify(convert(L, `+`)^(1/3))::integer and
  simplify(convert(L, `*`)^(1/3))::integer;
end proc:
select(filter, [$0..1000]); # Robert Israel, Jan 21 2019

Mathematica

cubeQ[n_] := IntegerQ[Surd[n, 3]]; aQ[n_] := cubeQ[Plus @@ IntegerDigits[n]] &&
cubeQ[Times @@ IntegerDigits[n]]; Select[Range[0, 3000], aQ] (* Amiram Eldar, Nov 20 2018 *)

Prog

(PARI) isok(n) = my(d=digits(n)); ispower(vecsum(d), 3) && ispower(vecprod(d), 3); \\ Michel Marcus, Nov 29 2018
(Magma) [n:n in [0..2000]| IsPower((&+Intseq(n)), 3) and IsPower((&*Intseq(n)), 3)] // Marius A. Burtea, Jan 21 2019

Crossrefs

Cf. A007953, A046031, A062398, A070276, A059094, A237767.

Sequence in context: A038288 A230111 A289664 * A204324 A070276 A002286

Adjacent sequences: A321878 A321879 A321880 * A321882 A321883 A321884

Keyword

nonn,base

Author

Enrique Navarrete, Nov 20 2018

Status

approved