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%I #15 Feb 22 2024 14:10:15
%S 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,
%T 97,421,431,521,541,631,641,643,653,743,751,761,821,842,853,862,863,
%U 941,953,961,971,983,5431,6421,6521,7321,7541,7621,7643,8431,8521
%N Numbers all of whose divisors have decimal digits in strictly decreasing order.
%C Sequence is finite. Last term a(104) = 98765431.
%C Subset of A009995 and A190220. Superset of A052014.
%H Nathaniel Johnston, <a href="/A190219/b190219.txt">Table of n, a(n) for n = 1..104</a> (full sequence)
%e Number 93 is in sequence because all divisors of 93 (1, 3, 31, 93) are numbers whose decimal digits are in strictly decreasing order.
%p 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
%t Select[Range[9000],Max[Flatten[Differences/@(IntegerDigits/@Divisors[#])]]<0&] (* _Harvey P. Dale_, Feb 22 2024 *)
%K nonn,fini,full,base
%O 1,2
%A _Jaroslav Krizek_, May 06 2011
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