A190221 Numbers all of whose divisors are numbers whose decimal digits are in nondecreasing order.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 125

Offset

1,2

Comments

Subset of A009994. Superset of A028864, A190218 and A190217.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

Example

Number 112 is in sequence because all divisors of 112 (1, 2, 4, 7, 8, 14, 16, 28, 56, 112) are numbers whose decimal digits are in nondecreasing order.

Maple

with(numtheory): A190221 := 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(A190221(n), n=1..64); # Nathaniel Johnston, May 06 2011

Mathematica

ndoQ[n_]:=Min[Differences[IntegerDigits[n]]]>=0; Select[Range[ 200], AllTrue[ Divisors[#], ndoQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2021 *)

Crossrefs

Sequence in context: A009994 A239016 A102827 * A239215 A055571 A132781

Adjacent sequences: A190218 A190219 A190220 * A190222 A190223 A190224

Keyword

nonn,base

Author

Jaroslav Krizek, May 06 2011

Status

approved