|
| |
|
|
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
|
| |
|
|
