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%I #18 Feb 11 2019 01:25:06
%S 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,
%T 36,37,38,39,45,46,47,48,49,56,57,58,59,67,68,69,78,79,89,125,127,134,
%U 135,136,137,138,139,145,149,157,158,167,169,178,179,235
%N Numbers all of whose divisors are numbers whose decimal digits are in strictly increasing order.
%C Sequence is finite. Last term a(163) = 23456789.
%C Subset of A009993. Superset of A052015.
%H Nathaniel Johnston and Jaroslav Krizek, <a href="/A190218/b190218.txt">Table of n, a(n) for n = 1..163</a> (complete list)
%e 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.
%p 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
%t Select[Range[250], And@@Positive[Flatten[Differences/@(IntegerDigits/@Divisors[#])]]&] (* _Harvey P. Dale_, Mar 24 2012 *)
%K nonn,fini,full,base
%O 1,2
%A _Jaroslav Krizek_, May 06 2011
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