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URL: https://oeis.org/A132067

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A132067
Composite integers m where d_{k+2} + d_k < 2*d_{k+1} for at least one k (1<=k<=A000005(m)-2), where d_k is the k-th positive divisor of m.
1
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
OFFSET
1,1
COMMENTS
In other words, the sequence contains those positive integers m where the difference (d_{k+1} - d_k) between some pair of consecutive positive divisors of m is greater than the difference (d_{k+2} - d_{k+1}) between the next pair of consecutive divisors of m.
LINKS
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 a term.
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 *)
PROG
(PARI) isok(n) = my(D = divisors(n), A = apply(x -> D[x] - D[x-1], [2..#D])); if(vecprod(apply(x -> A[x] >= A[x-1], [2..#A])) <> 1, 1, 0) \\ Miles Englezou, Jan 06 2026
CROSSREFS
Sequence in context: A107714 A029721 A224400 * A072989 A216603 A166730
KEYWORD
nonn
AUTHOR
Leroy Quet, Oct 30 2007
EXTENSIONS
Extended by Ray Chandler and Stefan Steinerberger, Nov 01 2007
STATUS
approved