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A237767 Product of digits of n is a nonzero cube. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 15 08:46 EDT 2022. Contains 356135 sequences. (Running on oeis4.)