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

1,1

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