A257225 - OEIS

%I #24 Sep 08 2022 08:46:12

%S 8,16,18,24,28,32,36,38,40,48,54,56,58,64,68,72,76,78,80,81,82,83,84,

%T 85,86,87,88,89,90,96,98,104,108,112,114,116,118,120,126,128,136,138,

%U 140,144,148,152,156,158,160,162,164,166,168,170,172,174,176,178

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

%C Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 8.

%C A011538 (numbers that contain an 8) is a subsequence. - _Michel Marcus_, May 19 2015

%F a(n) ~ n.

%e 18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 8.

%p select(t -> has(map(convert,numtheory:-divisors(t),base,10),8), [$1..200]); # _Robert Israel_, May 14 2015

%t Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 8] > 0 &]

%t Select[Range[200],SequenceCount[Flatten[IntegerDigits/@Divisors[#]],{8}]> 0&] (* _Harvey P. Dale_, Aug 02 2021 *)

%o (Magma) [n: n in [1..1000] | [8] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]

%o (PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 8), return(1))); 0

%o (Python)

%o from itertools import count, islice

%o from sympy import divisors

%o def A257225_gen(): return filter(lambda n:any('8' in str(d) for d in divisors(n, generator=True)), count(1))

%o A257225_list = list(islice(A257225_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), A257226 (9).

%K nonn,base

%O 1,1

%A _Jaroslav Krizek_, May 07 2015

%E Mathematica and PARI programs with assistance from _Michael De Vlieger_ and _Charles R Greathouse IV_, respectively.