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

8, 16, 18, 24, 28, 32, 36, 38, 40, 48, 54, 56, 58, 64, 68, 72, 76, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 96, 98, 104, 108, 112, 114, 116, 118, 120, 126, 128, 136, 138, 140, 144, 148, 152, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178

Offset: 1

Author

Jaroslav Krizek, May 07 2015

Keywords

• nonn
• base
• changed

Comments

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

A011538 (numbers that contain an 8) is a subsequence. - Michel Marcus, May 19 2015

Examples

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

Crossrefs

Cf. A037278, A176558, A243360, A256824.

Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257223 (6), A257224 (7), A257226 (9).

Programs

Magma

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

Maple

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

Mathematica

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 8] > 0 &]
Select[Range[200],SequenceCount[Flatten[IntegerDigits/@Divisors[#]],{8}]> 0&] (* Harvey P. Dale, Aug 02 2021 *)

PARI

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

Python

from itertools import count, islice
from sympy import divisors
def A257225_gen(): return filter(lambda n:any('8' in str(d) for d in divisors(n, generator=True)), count(1))
A257225_list = list(islice(A257225_gen(), 58)) # Chai Wah Wu, Dec 27 2021

Formula

a(n) ~ n.

Extensions

Mathematica and PARI programs with assistance from Michael De Vlieger and Charles R Greathouse IV, respectively.