A190219 Numbers all of whose divisors have decimal digits in strictly decreasing order.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 31, 40, 41, 43, 53, 61, 62, 63, 71, 73, 82, 83, 86, 93, 97, 421, 431, 521, 541, 631, 641, 643, 653, 743, 751, 761, 821, 842, 853, 862, 863, 941, 953, 961, 971, 983, 5431, 6421, 6521, 7321, 7541, 7621, 7643, 8431, 8521

Offset

1,2

Comments

Sequence is finite. Last term a(104) = 98765431.

Subset of A009995 and A190220. Superset of A052014.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..104 (full sequence)

Example

Number 93 is in sequence because all divisors of 93 (1, 3, 31, 93) are numbers whose decimal digits are in strictly decreasing order.

Maple

with(numtheory): A190219 := 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:=-1: 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(A190219(n), n=1..60); # Nathaniel Johnston, May 06 2011

Mathematica

Select[Range[9000], Max[Flatten[Differences/@(IntegerDigits/@Divisors[#])]]<0&] (* Harvey P. Dale, Feb 22 2024 *)

Crossrefs

Sequence in context: A032889 A308393 A009995 * A038367 A214958 A161350

Adjacent sequences: A190216 A190217 A190218 * A190220 A190221 A190222

Keyword

nonn,fini,full,base

Author

Jaroslav Krizek, May 06 2011

Status

approved