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A257225
Numbers that have at least one divisor containing the digit 8 in base 10.
7
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
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. 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
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