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

1,1

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.

Links

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

Formula

a(n) ~ n.

Example

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

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 *)

Prog

(Magma) [n: n in [1..1000] | [5] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
(PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 5), return(1))); 0
(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
(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

Crossrefs

Cf. A037278, A176558, A243360, A256824.

Sequence in context: A076311 A336483 A063284 * A092454 A350744 A248359

Adjacent sequences: A257219 A257220 A257221 * A257223 A257224 A257225

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