A206159 Numbers needing at most two digits to write all positive divisors in decimal representation.

1, 2, 3, 5, 7, 11, 13, 17, 19, 22, 31, 33, 41, 55, 61, 71, 77, 101, 113, 121, 131, 151, 181, 191, 199, 211, 311, 313, 331, 661, 811, 881, 911, 919, 991, 1111, 1117, 1151, 1171, 1181, 1511, 1777, 1811, 1999, 2111, 2221, 3313, 3331, 4111, 4441, 6661, 7177, 7717, 8111, 9199, 10111, 11113

Offset

1,2

Comments

The terms of A203897 having all divisors in A020449 (in particular, the first 1022 terms) are a subsequence. - M. F. Hasler, May 02 2022

Since 1 and the term itself are divisors, one must only check repdigits and those containing only 1 and another digit. - Michael S. Branicky, May 02 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..500 from M. F. Hasler)

Formula

A095048(a(n)) <= 2.

Mathematica

Select[Range[12000], Length[Union[Flatten[IntegerDigits/@Divisors[#]]]]<3&] (* Harvey P. Dale, May 03 2022 *)

Prog

(Python)
from sympy import divisors
def ok(n):
    digits_used = set()
    for d in divisors(n, generator=True):
        digits_used |= set(str(d))
        if len(digits_used) > 2: return False
    return True
print([k for k in range(1, 9000) if ok(k)]) # Michael S. Branicky, May 02 2022
(PARI) select( {is_A206159(n)=#Set(concat([digits(d)|d<-divisors(n)]))<3}, [1..10^4]) \\ M. F. Hasler, May 02 2022

Crossrefs

Cf. A027750, A031955, A011531, A106101, A004022, A062634.

Cf. A203897 (an "almost subsequence"), A020449 (primes with only digits 0 & 1), A095048 (number of distinct digits in divisors(n)).

Sequence in context: A152242 A166504 A095405 * A242127 A242126 A113581

Adjacent sequences: A206156 A206157 A206158 * A206160 A206161 A206162

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 05 2012

Extensions

Terms corrected by Harvey P. Dale, May 02 2022

Edited by N. J. A. Sloane, May 02 2022

Status

approved