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A094530 Numbers with exactly one arithmetic progression of four successive divisors (not necessarily consecutive). 2
12, 105, 140, 440, 585, 1729, 3825, 5643, 6380, 7161, 9009, 9867, 10472, 11408, 12025, 13923, 17732, 18705, 19760, 21505, 23715, 25568, 27489, 30272, 36465, 38665, 43472, 52521, 58995, 62307, 62985, 63308, 64467, 65780, 69345, 72105, 81075, 89425, 101065 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

m*a(n) = A094529(k) for all m>0 and some k.

LINKS

Table of n, a(n) for n=1..39.

EXAMPLE

Set of divisors of 440: {1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440}, there is only one arithmetic progression containing at least four terms: {2,5,8,11} = (2+k*3:0<=k<3), therefore 440 is a term.

MATHEMATICA

oap4Q[n_]:=Length[Select[Subsets[Divisors[n], {4}], Length[Union[ Differences[ #]]]==1&]]==1; Select[Range[102000], oap4Q] (* Harvey P. Dale, Aug 02 2017 *)

CROSSREFS

Cf. A091012, A094529.

Sequence in context: A334168 A220111 A353549 * A157024 A051815 A004321

Adjacent sequences:  A094527 A094528 A094529 * A094531 A094532 A094533

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 07 2004

STATUS

approved

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)