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

1,1

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

Links

Table of n, a(n) for n=1..58.

Formula

a(n) ~ n.

Example

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

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 *)

Prog

(Magma) [n: n in [1..1000] | [8] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
(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(), 20)) # Chai Wah Wu, Dec 27 2021

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).

Sequence in context: A357002 A356441 A140270 * A092456 A232724 A260409

Adjacent sequences: A257222 A257223 A257224 * A257226 A257227 A257228

Keyword

nonn,base

Author

Jaroslav Krizek, May 07 2015

Extensions

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

Status

approved