A094529 -id:A094529 - cp's OEIS frontend

A094530 Numbers with exactly one arithmetic progression of four successive divisors (not necessarily consecutive).

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

Offset: 1

Reinhard Zumkeller, May 07 2004

nonn

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

			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.

Cf. A091012, A094529.

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

A270571 Numbers with at least one arithmetic progression of four consecutive divisors.

Original entry on oeis.org

12, 24, 36, 48, 60, 72, 84, 96, 105, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 315, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 525, 528, 540, 552, 564, 576, 588, 600

Offset: 1

Reinhard Zumkeller, Mar 19 2016

nonn

Contrast A094529 where the divisors in arithmetic progression do not have to be consecutive.

			348 is included because its divisors are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348, and the first four are in arithmetic progression.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A091011, A094529, A094530.

ap4dQ[n_]:=Count[Partition[Divisors[n],4,1],_?(Length[ Union[ Differences[ #]]] == 1&)]>0; Select[ Range[700],ap4dQ]

Edited by Harvey P. Dale and Alois P. Heinz, Mar 19 2016

cp's OEIS Frontend

A094530 Numbers with exactly one arithmetic progression of four successive divisors (not necessarily consecutive).

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