

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

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


LINKS



FORMULA



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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



