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A257226
Numbers that have at least one divisor containing the digit 9 in base 10.
7
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.
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. 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
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, May 29 2015
STATUS
approved