A237767 Product of digits of n is a nonzero cube.

1, 8, 11, 18, 24, 39, 42, 81, 88, 93, 111, 118, 124, 139, 142, 181, 188, 193, 214, 222, 241, 248, 284, 319, 333, 389, 391, 398, 412, 421, 428, 444, 469, 482, 496, 555, 649, 666, 694, 777, 811, 818, 824, 839, 842, 881, 888, 893, 913, 931

Offset

1,2

Comments

No number with a 0 in it (A011540) can be in this sequence. If a number is in this sequence, then so is its reversal of digits (A004086) and other permutations of its digits. - Alonso del Arte, Feb 20 2014

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

There are between 9^(k-6) and 9^k k-digit members of this sequence, so a(n) >> n^1.04 and in particular this sequence has density 0. - Charles R Greathouse IV, Feb 21 2014

Example

3*9*1 = 27 = 3^3, thus 391 is a member of this sequence.
3*9*8 = 216 = 6^3, thus 398 is a member of this sequence.
4*2*8 = 64 = 4^3, thus 428 is a member of this sequence.

Mathematica

pdcQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&IntegerQ[ Surd[ Times@@idn, 3]]]; Select[Range[1000], pdcQ] (* Harvey P. Dale, Aug 25 2017 *)

Prog

(Python)
def DigitProd(x):
..total = 1
..for i in str(x):
....total *= int(i)
..return total
def Cube(x):
..for n in range(1, 10**3):
....if DigitProd(x) == n**3:
......return True
....if DigitProd(x) < n**3:
......return False
..return False
x = 1
while x < 1000:
..if Cube(x):
....print(x)
..x += 1
(PARI)
s=[]; for(n=1, 1000, t=eval(Vec(Str(n))); d=prod(i=1, #t, t[i]); if(d>0 && ispower(d, 3), s=concat(s, n))); s \\ Colin Barker, Feb 17 2014

Crossrefs

Cf. A007954, A050626.

Sequence in context: A291663 A306277 A067469 * A284324 A205856 A318079

Adjacent sequences: A237764 A237765 A237766 * A237768 A237769 A237770

Keyword

nonn,base

Author

Derek Orr, Feb 12 2014

Status

approved