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

Author

Jaroslav Krizek, May 06 2011

Keywords

• nonn
• fini
• full
• base

Comments

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

Subset of A009993. Superset of A052015.

Examples

			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.
		

Links

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

Programs

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 *)