A237767 -id:A237767 - cp's OEIS frontend

A067070 Cubes whose product of digits is a cube > 0.

1, 8, 24389, 226981, 9393931, 11239424, 17373979, 36264691, 66923416, 94818816, 348913664, 435519512, 463684824, 549353259, 555412248, 743677416, 3929352552, 4982686912, 5526456832, 11329982936, 12374478297, 12681938368, 15142552424

Offset: 1

Amarnath Murthy, Jan 05 2002

			24389 is in the sequence because (1) it is a cube and (2) the product of its digits is 2*4*3*8*9, = 1728 which is a cube > 0.

Felice Russo, A set of new Smarandache Functions, Sequences and conjectures in number theory, American Research Press, Lupton USA.

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Intersection of A237767 and A000578.

Cf. A007954, A052045, A052382, A067071.

pdcQ[n_]:=Module[{pd=Times@@IntegerDigits[n]},pd>0&&IntegerQ[ Surd[ pd,3]]]; Select[Range[3000]^3,pdcQ] (* Harvey P. Dale, Jun 01 2015 *)

isA237767(k)={my(p=vecprod(digits(k))); p && ispower(p,3)}
{ for (m=1, 2500, if(isA237767(m^3), print1(m^3, ", "))) } \\ Harry J. Smith, May 04 2010

first(n) = {
     my(res = List(), c, vp, i);
     for(i = 1, oo,
          c = i^3;
          vp = vecprod(digits(c));
          if(vp && ispower(vp,3),
               listput(res, c);
               if(#res >= n,
                    return(Vec(res))
               )
          )
     )
} \\ David A. Corneth, Dec 01 2023

a(n) = A067071(n)^3. - Andrew Howroyd, Dec 05 2024

More terms from Sascha Kurz, Mar 23 2002
One further term from Luc Stevens (lms022(AT)yahoo.com), May 03 2006
Edited by R. J. Mathar, Aug 08 2008
Offset changed from 0 to 1 by Harry J. Smith, May 04 2010

A321881 Numbers whose sum and product of digits are cubes.

Original entry on oeis.org

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

Enrique Navarrete, Nov 20 2018

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.

			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).

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

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

[n:n in [0..2000]| IsPower((&+Intseq(n)), 3) and IsPower((&*Intseq(n)), 3)] // Marius A. Burtea, Jan 21 2019

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

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 *)

isok(n) = my(d=digits(n)); ispower(vecsum(d), 3) && ispower(vecprod(d), 3); \\ Michel Marcus, Nov 29 2018

A385056 Prime numbers whose digit product is a positive cube.

Original entry on oeis.org

11, 139, 181, 193, 241, 389, 421, 811, 839, 881, 983, 1181, 1193, 1319, 1777, 1811, 1913, 1931, 1999, 2141, 2221, 2269, 2411, 2663, 3119, 3191, 3313, 3331, 3463, 3643, 3833, 3889, 3911, 4211, 4363, 4441, 4691, 6229, 6263, 6343, 6491, 6661, 7177, 7717, 7877, 8111

Offset: 1

Mohd Anwar Jamal Faiz, Jun 16 2025

Intersection of A000040 and A237767.
Subsequence of A038618.
Cf. A184328.

q:= n-> isprime(n) and (p-> p>0 and iroot(p, 3)^3=p)(mul(i, i=convert(n, base, 10))):
select(q, [$2..10000])[];  # Alois P. Heinz, Jun 16 2025

q[n_] := Module[{pd = Times @@ IntegerDigits[n]}, pd > 0 && IntegerQ[Surd[pd, 3]]]; Select[Prime[Range[1300]], q] (* Amiram Eldar, Jun 16 2025 *)

isok(k) = if (isprime(k), my(p=vecprod(digits(k))); p && ispower(p, 3)); \\ Michel Marcus, Jun 16 2025

from sympy import primerange, integer_nthroot
from math import prod
is_cube = lambda n: n > 0 and integer_nthroot(n, 3)[1]
digit_product = lambda n: prod(map(int, str(n)))
cubigit_primes = [p for p in primerange(2, 100000) if is_cube(dp := digit_product(p))]
print(cubigit_primes)

cp's OEIS Frontend

A067070 Cubes whose product of digits is a cube > 0.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A321881 Numbers whose sum and product of digits are cubes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

A385056 Prime numbers whose digit product is a positive cube.

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

PARI

Python