cp's OEIS Frontend

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

%I A257222 #19 Dec 15 2024 19:38:26
%S A257222 5,10,15,20,25,30,35,40,45,50,51,52,53,54,55,56,57,58,59,60,65,70,75,
%T A257222 80,85,90,95,100,102,104,105,106,108,110,112,114,115,116,118,120,125,
%U A257222 130,135,140,145,150,151,152,153,154,155,156,157,158,159,160,162,165
%N A257222 Numbers that have at least one divisor containing the digit 5 in base 10.
%C A257222 Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 5.
%C A257222 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.
%F A257222 a(n) ~ n.
%e A257222 20 is in sequence because the list of divisors of 20: (1, 2, 4, 5, 10, 20) contains digit 5.
%t A257222 Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 5] > 0 &]
%t A257222 Select[Range[200],Max[DigitCount[Divisors[#],10,5]]>0&] (* _Harvey P. Dale_, Sep 15 2018 *)
%o A257222 (Magma) [n: n in [1..1000] | [5] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];
%o A257222 (PARI) is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 5), return(1))); 0
%o A257222 (Python)
%o A257222 from sympy import divisors
%o A257222 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
%o A257222 (Perl) use ntheory ":all"; for my $n (1..1000) { say $n if scalar(grep {/5/} divisors($n)) } # _Dana Jacobsen_, May 07 2015
%o A257222 (Perl) use ntheory ":all"; my @a257222 = grep { scalar(grep {/5/} divisors($_)) } 1..1000; # _Dana Jacobsen_, May 07 2015
%Y A257222 Cf. A037278, A176558, A243360, A256824.
%K A257222 nonn,base
%O A257222 1,1
%A A257222 _Jaroslav Krizek_, May 05 2015
%E A257222 Mathematica and PARI programs with assistance from _Michael De Vlieger_ and _Charles R Greathouse IV_, respectively.