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A270308
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Numbers which are less than the number of their ordered factorizations.
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3
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72, 96, 120, 144, 192, 216, 240, 288, 336, 360, 384, 432, 480, 504, 540, 576, 600, 648, 672, 720, 768, 840, 864, 960, 1008, 1080, 1152, 1200, 1260, 1296, 1344, 1440, 1512, 1536, 1584, 1620, 1680, 1728, 1800, 1872, 1920, 1944, 2016, 2112, 2160, 2240, 2304, 2400
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OFFSET
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1,1
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COMMENTS
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Also numbers which are less than the number of their perfect factorizations or gozinta chains.
The least odd term of this sequence is 51288546684375. - Amiram Eldar, Apr 11 2020
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LINKS
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FORMULA
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EXAMPLE
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The ordered partitions of 72 are 76, of 96 are 112, of 120 are 132, etc.
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MAPLE
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P:=proc(q) local a, j, k, m; a:= array(1..q); for k from 1 to q do a[k]:=0 od; a[1]:=1;
for j from 2 to q do for m from 1 to j-1 do if j mod m=0 then a[j]:= a[j]+a[m]; fi; od;
if j<a[j] then print(j); fi; od; end: P(10^5);
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MATHEMATICA
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f[1] = 1; f[n_] := DivisorSum[n, f[#] &, # < n &]; Select[Range[2400], f[#] > # &] (* Amiram Eldar, Apr 11 2020 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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