A257226 Numbers that have at least one divisor containing the digit 9 in base 10.

9, 18, 19, 27, 29, 36, 38, 39, 45, 49, 54, 57, 58, 59, 63, 69, 72, 76, 78, 79, 81, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 108, 109, 114, 116, 117, 118, 119, 126, 129, 133, 135, 138, 139, 144, 145, 147, 149, 152, 153, 156, 158, 159, 162, 169, 171, 174

Offset

1,1

Comments

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 9.

A011539 (numbers that contain a 9) is a subsequence.

Links

Table of n, a(n) for n=1..59.

Formula

a(n) ~ n.

Example

18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 9.

Mathematica

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 9] > 0 &] (* after Michael De Vlieger *)

Prog

(Magma) [n: n in [1..1000] | [9] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
(PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 9), return(1))); 0 \\ after Charles R Greathouse IV
(Python)
from itertools import count, islice
from sympy import divisors
def A257226_gen(): return filter(lambda n:any('9' in str(d) for d in divisors(n, generator=True)), count(1))
A257226_list = list(islice(A257226_gen(), 20)) # Chai Wah Wu, Dec 27 2021

Crossrefs

Cf. A037278, A176558, A243360, A256824.

Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257223 (6), A257224 (7), A257225 (8).

Sequence in context: A296711 A297144 A107977 * A092457 A062057 A254066

Adjacent sequences: A257223 A257224 A257225 * A257227 A257228 A257229

Keyword

nonn,base

Author

Jaroslav Krizek, May 29 2015

Status

approved