A257223 Numbers that have at least one divisor containing the digit 6 in base 10.

6, 12, 16, 18, 24, 26, 30, 32, 36, 42, 46, 48, 52, 54, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 76, 78, 80, 84, 86, 90, 92, 96, 102, 104, 106, 108, 112, 114, 116, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 144, 146, 150, 152, 156, 160, 161, 162

Offset

1,1

Comments

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 6.

A011536 (numbers that contain a 6) is a subsequence. - Michel Marcus, May 25 2015

Links

Table of n, a(n) for n=1..59.

Formula

a(n) ~ n.

Example

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

Mathematica

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 6] > 0 &]
Select[Range[200], Count[Flatten[IntegerDigits/@Divisors[#]], 6]>0&] (* Harvey P. Dale, Nov 05 2021 *)

Prog

(Magma) [n: n in [1..1000] | [6] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
(PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 6), return(1))); 0

Crossrefs

Cf. A037278, A176558, A243360, A256824.

Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257224 (7), A257225 (8), A257226 (9).

Sequence in context: A315623 A315624 A013637 * A092455 A315625 A315626

Adjacent sequences: A257220 A257221 A257222 * A257224 A257225 A257226

Keyword

nonn,base

Author

Jaroslav Krizek, May 05 2015

Extensions

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

Status

approved