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A257222 Numbers n that have at least one divisor containing the digit 5 in base 10. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n whose concatenation of divisors A037278(n), A176558(n), A243360(n) or A256824(n) contains a digit 5.

Sequences of numbers n whose concatenation of divisors contains a digit k in base 10 for 0 <= k <= 9: A209932 for k = 0, A000027 for k = 1, A257219 for k = 2, A257220 for k = 3, A257221 for k = 4, A257222 for k = 5, A257223 for k = 6, A257224 for k = 7, A257225 for k = 8, A257226 for k = 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: A313733 A076311 A063284 * A092454 A248359 A008706

Adjacent sequences:  A257219 A257220 A257221 * A257223 A257224 A257225

KEYWORD

nonn,base

AUTHOR

Jaroslav Krizek, May 05 2015

EXTENSIONS

Programs MATHEMATICA and PARI with assistance by Michael De Vlieger and Charles R Greathouse IV respectively.

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)