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 A257219 Numbers that have at least one divisor containing the digit 2 in base 10. 8
 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 2. 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. 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 A011532 (numbers that contain a 2) is a subsequence. - Michel Marcus, May 19 2015 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 FORMULA a(n) ~ n. - Charles R Greathouse IV, Apr 22 2015 EXAMPLE 18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 2. 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 MATHEMATICA Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 2] > 0 &] (* Michael De Vlieger, Apr 20 2015 *) PROG (Magma) [n: n in [1..1000] | [2] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))] (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 CROSSREFS Cf. A037278, A176558, A243360, A256824. Sequence in context: A055960 A351626 A007928 * A092451 A214673 A055962 Adjacent sequences: A257216 A257217 A257218 * A257220 A257221 A257222 KEYWORD nonn,base AUTHOR Jaroslav Krizek, Apr 20 2015 STATUS approved

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Last modified May 29 10:21 EDT 2024. Contains 372927 sequences. (Running on oeis4.)