A190218 Numbers all of whose divisors are numbers whose decimal digits are in strictly increasing order.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 125, 127, 134, 135, 136, 137, 138, 139, 145, 149, 157, 158, 167, 169, 178, 179, 235

Offset

1,2

Comments

Sequence is finite. Last term a(163) = 23456789.

Subset of A009993. Superset of A052015.

Links

Nathaniel Johnston and Jaroslav Krizek, Table of n, a(n) for n = 1..163 (complete list)

Example

Number 135 is in sequence because all divisors of 135 (1, 3, 5, 9, 15, 27, 45, 135) are numbers whose decimal digits are in strictly increasing order.

Maple

with(numtheory): A190218 := proc(n) option remember: local d, dd, i, j, k, m, poten: if(n=1)then return 1: fi: for k from procname(n-1)+1 do d:=divisors(k): poten:=1: for i from 1 to nops(d) do m:=10: dd:=convert(d[i], base, 10): for j from 1 to nops(dd) do if(m>dd[j])then m:=dd[j]: else poten:=0: break: fi: od: if(poten=0)then break:fi: od: if(poten=1)then return k: fi: od: end: seq(A190218(n), n=1..62); # Nathaniel Johnston, May 06 2011

Mathematica

Select[Range[250], And@@Positive[Flatten[Differences/@(IntegerDigits/@Divisors[#])]]&] (* Harvey P. Dale, Mar 24 2012 *)

Crossrefs

Sequence in context: A239216 A032848 A009993 * A055569 A351119 A277046

Adjacent sequences: A190215 A190216 A190217 * A190219 A190220 A190221

Keyword

nonn,fini,full,base

Author

Jaroslav Krizek, May 06 2011

Status

approved