A237767 - OEIS

%I #17 Aug 25 2017 10:38:11

%S 1,8,11,18,24,39,42,81,88,93,111,118,124,139,142,181,188,193,214,222,

%T 241,248,284,319,333,389,391,398,412,421,428,444,469,482,496,555,649,

%U 666,694,777,811,818,824,839,842,881,888,893,913,931

%N Product of digits of n is a nonzero cube.

%C 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

%H Harvey P. Dale, <a href="/A237767/b237767.txt">Table of n, a(n) for n = 1..1000</a>

%F 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

%e 3*9*1 = 27 = 3^3, thus 391 is a member of this sequence.

%e 3*9*8 = 216 = 6^3, thus 398 is a member of this sequence.

%e 4*2*8 = 64 = 4^3, thus 428 is a member of this sequence.

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

%o (Python)

%o def DigitProd(x):

%o ..total = 1

%o ..for i in str(x):

%o ....total *= int(i)

%o ..return total

%o def Cube(x):

%o ..for n in range(1,10**3):

%o ....if DigitProd(x) == n**3:

%o ......return True

%o ....if DigitProd(x) < n**3:

%o ......return False

%o ..return False

%o x = 1

%o while x < 1000:

%o ..if Cube(x):

%o ....print(x)

%o ..x += 1

%o (PARI)

%o 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

%Y Cf. A007954, A050626.

%K nonn,base

%O 1,2

%A _Derek Orr_, Feb 12 2014