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A206159
Numbers needing at most two digits to write all positive divisors in decimal representation.
4
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. 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
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