A257222 Numbers that have at least one divisor containing the digit 5 in base 10.

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 65, 70, 75, 80, 85, 90, 95, 100, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 118, 120, 125, 130, 135, 140, 145, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 162, 165

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 5.

Sequences of numbers k whose concatenation of divisors contains a digit j in base 10 for 0 <= j <= 9: A209932 for j = 0, A000027 for j = 1, A257219 for j = 2, A257220 for j = 3, A257221 for j = 4, A257222 for j = 5, A257223 for j = 6, A257224 for j = 7, A257225 for j = 8, A257226 for j = 9.

Examples

			20 is in sequence because the list of divisors of 20: (1, 2, 4, 5, 10, 20) contains digit 5.
		

Crossrefs

Cf. A037278, A176558, A243360, A256824.

Programs

Magma

[n: n in [1..1000] | [5] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];

Mathematica

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 5] > 0 &]
Select[Range[200],Max[DigitCount[Divisors[#],10,5]]>0&] (* Harvey P. Dale, Sep 15 2018 *)

PARI

is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 5), return(1))); 0

Perl

use ntheory ":all"; for my $n (1..1000) { say $n if scalar(grep {/5/} divisors($n)) } # Dana Jacobsen, May 07 2015

Perl

use ntheory ":all"; my @a257222 = grep { scalar(grep {/5/} divisors($)) } 1..1000; # _Dana Jacobsen, May 07 2015

Python

from sympy import divisors
A257222_list = [n for n in range(1,10**3) if '5' in set().union(*(set(str(d)) for d in divisors(n,generator=True)))] # Chai Wah Wu, May 06 2015

Formula

a(n) ~ n.

Extensions

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