cp's OEIS Frontend

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

%I A257226 #23 Aug 29 2025 10:55:51
%S A257226 9,18,19,27,29,36,38,39,45,49,54,57,58,59,63,69,72,76,78,79,81,87,89,
%T A257226 90,91,92,93,94,95,96,97,98,99,108,109,114,116,117,118,119,126,129,
%U A257226 133,135,138,139,144,145,147,149,152,153,156,158,159,162,169,171,174
%N A257226 Numbers that have at least one divisor containing the digit 9 in base 10.
%C A257226 Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 9.
%C A257226 A011539 (numbers that contain a 9) is a subsequence.
%F A257226 a(n) ~ n.
%e A257226 18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 9.
%t A257226 Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 9] > 0 &] (* after _Michael De Vlieger_ *)
%o A257226 (Magma) [n: n in [1..1000] | [9] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];
%o A257226 (PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 9), return(1))); 0 \\ after _Charles R Greathouse IV_
%o A257226 (Python)
%o A257226 from itertools import count, islice
%o A257226 from sympy import divisors
%o A257226 def A257226_gen(): return filter(lambda n:any('9' in str(d) for d in divisors(n,generator=True)),count(1))
%o A257226 A257226_list = list(islice(A257226_gen(),20)) # _Chai Wah Wu_, Dec 27 2021
%Y A257226 Cf. A037278, A176558, A243360, A256824.
%Y A257226 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 A257226 nonn,base,changed
%O A257226 1,1
%A A257226 _Jaroslav Krizek_, May 29 2015