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%I #30 Sep 08 2022 08:46:12
%S 2,4,6,8,10,12,14,16,18,20,21,22,23,24,25,26,27,28,29,30,32,34,36,38,
%T 40,42,44,46,48,50,52,54,56,58,60,62,63,64,66,68,69,70,72,74,75,76,78,
%U 80,81,82,84,86,87,88,90,92,94,96,98,100,102,104,105,106,108
%N Numbers that have at least one divisor containing the digit 2 in base 10.
%C Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 2.
%C 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.
%C All even numbers and all numbers which have a digit "2" themselves are trivially in this sequence. The first terms not of this form are the odd multiples of odd numbers between 21 and 29: { 63 = 3*21, 69 = 3*23, 75 = 3*25, 81 = 3*27, 87 = 3*29, 105 = 5*21, 115 = 5*23, 135 = 5*27, 145 = 5*29, ...}. - _M. F. Hasler_, Apr 22 2015
%C A011532 (numbers that contain a 2) is a subsequence. - _Michel Marcus_, May 19 2015
%H Charles R Greathouse IV, <a href="/A257219/b257219.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ n. - _Charles R Greathouse IV_, Apr 22 2015
%e 18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 2.
%e In the same way all even numbers have the divisor 2 and thus are in this sequence; numbers N in { 20,...,29, 120,...,129, 200,...,299 } have the digit 2 in N which is divisor of itself. - _M. F. Hasler_, Apr 22 2015
%t Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 2] > 0 &] (* _Michael De Vlieger_, Apr 20 2015 *)
%o (Magma) [n: n in [1..1000] | [2] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
%o (PARI) is(n)=!bittest(n,0)||setsearch(Set(digits(n)),2)||fordiv(n,d,setsearch(Set(digits(d)),2)&&return(1)) \\ _M. F. Hasler_, Apr 22 2015
%Y Cf. A037278, A176558, A243360, A256824.
%K nonn,base
%O 1,1
%A _Jaroslav Krizek_, Apr 20 2015
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