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A257225 Numbers that have at least one divisor containing the digit 8 in base 10.

%I A257225 #32 Sep 04 2025 05:02:41
%S A257225 8,16,18,24,28,32,36,38,40,48,54,56,58,64,68,72,76,78,80,81,82,83,84,
%T A257225 85,86,87,88,89,90,96,98,104,108,112,114,116,118,120,126,128,136,138,
%U A257225 140,144,148,152,156,158,160,162,164,166,168,170,172,174,176,178
%N A257225 Numbers that have at least one divisor containing the digit 8 in base 10.
%C A257225 Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 8.
%C A257225 A011538 (numbers that contain an 8) is a subsequence. - _Michel Marcus_, May 19 2015
%F A257225 a(n) ~ n.
%e A257225 18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 8.
%p A257225 select(t -> has(map(convert,numtheory:-divisors(t),base,10),8), [$1..200]); # _Robert Israel_, May 14 2015
%t A257225 Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 8] > 0 &]
%t A257225 Select[Range[200],SequenceCount[Flatten[IntegerDigits/@Divisors[#]],{8}]> 0&] (* _Harvey P. Dale_, Aug 02 2021 *)
%o A257225 (Magma) [n: n in [1..1000] | [8] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];
%o A257225 (PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 8), return(1))); 0
%o A257225 (Python)
%o A257225 from itertools import count, islice
%o A257225 from sympy import divisors
%o A257225 def A257225_gen(): return filter(lambda n:any('8' in str(d) for d in divisors(n, generator=True)), count(1))
%o A257225 A257225_list = list(islice(A257225_gen(), 58)) # _Chai Wah Wu_, Dec 27 2021
%Y A257225 Cf. A037278, A176558, A243360, A256824.
%Y A257225 Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257223 (6), A257224 (7), A257226 (9).
%K A257225 nonn,base,changed
%O A257225 1,1
%A A257225 _Jaroslav Krizek_, May 07 2015
%E A257225 Mathematica and PARI programs with assistance from _Michael De Vlieger_ and _Charles R Greathouse IV_, respectively.