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%I #19 Sep 08 2022 08:46:12
%S 9,18,19,27,29,36,38,39,45,49,54,57,58,59,63,69,72,76,78,79,81,87,89,
%T 90,91,92,93,94,95,96,97,98,99,108,109,114,116,117,118,119,126,129,
%U 133,135,138,139,144,145,147,149,152,153,156,158,159,162,169,171,174
%N Numbers that have at least one divisor containing the digit 9 in base 10.
%C Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 9.
%C A011539 (numbers that contain a 9) is a subsequence.
%F a(n) ~ n.
%e 18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 9.
%t Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 9] > 0 &] (* after _Michael De Vlieger_ *)
%o (Magma) [n: n in [1..1000] | [9] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
%o (PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 9), return(1))); 0 \\ after _Charles R Greathouse IV_
%o (Python)
%o from itertools import count, islice
%o from sympy import divisors
%o def A257226_gen(): return filter(lambda n:any('9' in str(d) for d in divisors(n,generator=True)),count(1))
%o A257226_list = list(islice(A257226_gen(),20)) # _Chai Wah Wu_, Dec 27 2021
%Y Cf. A037278, A176558, A243360, A256824.
%Y Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257223 (6), A257224 (7), A257225 (8).
%K nonn,base
%O 1,1
%A _Jaroslav Krizek_, May 29 2015
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