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

Author

Reinhard Zumkeller, May 07 2004

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A091012, A094529.

Programs

Mathematica

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