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

Author

Jaroslav Krizek, May 05 2015

Keywords

• nonn
• base

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

Examples

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

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).

Programs

Magma

[n: n in [1..1000] | [6] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];

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 *)

PARI

is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 6), return(1))); 0

Formula

a(n) ~ n.

Extensions

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