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
Examples
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.
Links
- Nathaniel Johnston, Table of n, a(n) for n = 1..1000
Programs
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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
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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 *)
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