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A132067 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. 0
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; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..55.

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.

MATHEMATICA

f[n_] := Block[{d}, d = Divisors[n]; d - Prepend[Most[d], 0]]; Flatten[Position[OrderedQ /@ Array[f, 260], False]] (* Ray Chandler, Nov 01 2007 *)

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, Oct 31 2007 *)

CROSSREFS

Sequence in context: A107714 A029721 A224400 * A072989 A216603 A166730

Adjacent sequences:  A132064 A132065 A132066 * A132068 A132069 A132070

KEYWORD

nonn

AUTHOR

Leroy Quet, Oct 30 2007

EXTENSIONS

Extended by Ray Chandler and Stefan Steinerberger, Nov 01 2007

STATUS

approved

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Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)