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A257221 Numbers that have at least one divisor containing the digit 4 in base 10.

%I A257221 #19 Sep 08 2022 08:46:12
%S A257221 4,8,12,14,16,20,24,28,32,34,36,40,41,42,43,44,45,46,47,48,49,52,54,
%T A257221 56,60,64,68,70,72,74,76,80,82,84,86,88,90,92,94,96,98,100,102,104,
%U A257221 108,112,114,116,120,123,124,126,128,129,132,134,135,136,138,140,141
%N A257221 Numbers that have at least one divisor containing the digit 4 in base 10.
%C A257221 Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 4.
%C A257221 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.
%H A257221 Charles R Greathouse IV, <a href="/A257221/b257221.txt">Table of n, a(n) for n = 1..10000</a>
%F A257221 a(n) ~ n. - _Charles R Greathouse IV_, Apr 30 2015
%e A257221 16 is in sequence because the list of divisors of 16: (1, 2, 4, 8, 16) contains digit 4.
%t A257221 Select[Range@ 141, Part[Plus @@ DigitCount@ Divisors@ #, 4] > 0 &] (* _Michael De Vlieger_, Apr 20 2015 *)
%t A257221 Select[Range[200],Count[Flatten[IntegerDigits/@Divisors[#]],4]>0&] (* _Harvey P. Dale_, May 05 2022 *)
%o A257221 (Magma) [n: n in [1..1000] | [4] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
%o A257221 (PARI) is(n)=fordiv(n,d, if(setsearch(Set(digits(d)),4), return(1))); 0 \\ _Charles R Greathouse IV_, Apr 30 2015
%Y A257221 Cf. A037278, A176558, A243360, A256824.
%K A257221 nonn,base
%O A257221 1,1
%A A257221 _Jaroslav Krizek_, Apr 20 2015