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A190219
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Numbers all of whose divisors have decimal digits in strictly decreasing order.
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5
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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
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OFFSET
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1,2
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COMMENTS
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Sequence is finite. Last term a(104) = 98765431.
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LINKS
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EXAMPLE
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Number 93 is in sequence because all divisors of 93 (1, 3, 31, 93) are numbers whose decimal digits are in strictly decreasing order.
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MAPLE
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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
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MATHEMATICA
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Select[Range[9000], Max[Flatten[Differences/@(IntegerDigits/@Divisors[#])]]<0&] (* Harvey P. Dale, Feb 22 2024 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full,base
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AUTHOR
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STATUS
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approved
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