A066640 Numbers such that all divisors have only odd digits.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 31, 33, 35, 37, 39, 51, 53, 55, 57, 59, 71, 73, 77, 79, 91, 93, 95, 97, 99, 111, 113, 117, 119, 131, 133, 137, 139, 151, 153, 155, 157, 159, 171, 173, 177, 179, 191, 193, 197, 199

Offset: 1

Author

Amarnath Murthy, Dec 28 2001

Keywords

• nonn
• base

Comments

Is this sequence infinite? - Charles R Greathouse IV, Sep 07 2012

Examples

			77 = 11 * 7 belongs to this sequence but 75 does not as 25 (with a 2) divides 75.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A014261. A030096 is a subsequence.

Programs

Mathematica

Select[Range[250], And@@OddQ/@Flatten[IntegerDigits/@Divisors[ # ]]&]

PARI

f(n)=vecmin(Vec(Vecsmall(Str(n)))%2)
is(n)=fordiv(n,d,if(!f(d),return(0)));1 \\ Charles R Greathouse IV, Sep 07 2012

Python

from itertools import islice, count
from sympy import divisors
def A066640(): return filter(lambda n: all(set(str(m)) <= {'1','3','5','7','9'} for m in divisors(n,generator=True)), count(1,2))
A066640_list = list(islice(A066640(),20)) # Chai Wah Wu, Nov 22 2021

Extensions

Corrected and extended by Harvey P. Dale, Jan 01 2002