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.
MAPLE
filter:= proc(n) local T;
T:= Statistics:-Tally(convert(n, base, 10), output=table);
if assigned(T[0]) then return false fi;
eval(T[2] + 2*T[4] + T[6] mod 3, T = [0$6]) = 0
and eval(T[3] + T[6] + 2*T[9] mod 3, T = [0$9]) = 0
and member(T[5] mod 3, [0, 'T[5]'])
and member(T[7] mod 3, [0, 'T[7]'])
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 16 2025
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
(Python)
from math import prod
from sympy import integer_nthroot
def ok(n): return (p:=prod(map(int, str(n)))) > 0 and integer_nthroot(p, 3)[1]
print([k for k in range(10**3) if ok(k)]) # Michael S. Branicky, Jun 16 2025
(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
KEYWORD
nonn,base
AUTHOR
Derek Orr, Feb 12 2014
EXTENSIONS
Name edited by Michel Marcus, Jun 16 2025
STATUS
approved
