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A132067
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Composite integers n where d_{k+2} + d_k < 2*d_{k+1} for at least one k (1<=k<=A000005(n)-2), where d_k is the k-th positive divisor of n.
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0
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20, 30, 35, 40, 42, 56, 60, 63, 70, 72, 77, 80, 84, 88, 90, 99, 100, 105, 110, 112, 117, 120, 126, 130, 132, 140, 143, 144, 150, 154, 156, 160, 165, 168, 175, 176, 180, 182, 187, 189, 195, 198, 200, 204, 208, 209, 210, 216, 220, 221, 224, 238, 240, 245, 247
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| In other words, the sequence contains those positive integers n where the difference (d_{k+1} - d_k) between some pair of consecutive positive divisors of n is greater than the difference (d_{k+2} - d_{k+1}) between the next pair of consecutive divisors of n.
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EXAMPLE
| The positive divisors of 20 are 1,2,4,5,10,20. d_2 + d_4 = 2 + 5 is < 2 * d_3 = 2 * 4. So 20 is in the sequence.
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MATHEMATICA
| f[n_] := Block[{d}, d = Divisors[n]; d - Prepend[Most[d], 0]]; Flatten[Position[OrderedQ /@ Array[f, 260], False]] (*Chandler*)
a = {}; For[n = 1, n < 1000, n++, c = 0; For[j = 1, j < Length[Divisors[n]] - 1, j++, If[Divisors[n][[j]] + Divisors[n][[j + 2]] < 2*Divisors[n][[j + 1]], c = 1]]; If[c == 1, AppendTo[a, n]]]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 31 2007
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CROSSREFS
| Sequence in context: A171908 A107714 A029721 * A072989 A166730 A109944
Adjacent sequences: A132064 A132065 A132066 * A132068 A132069 A132070
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Oct 30 2007
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 01 2007
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