A115017 a(n) = largest triangular number dividing n.

1, 1, 3, 1, 1, 6, 1, 1, 3, 10, 1, 6, 1, 1, 15, 1, 1, 6, 1, 10, 21, 1, 1, 6, 1, 1, 3, 28, 1, 15, 1, 1, 3, 1, 1, 36, 1, 1, 3, 10, 1, 21, 1, 1, 45, 1, 1, 6, 1, 10, 3, 1, 1, 6, 55, 28, 3, 1, 1, 15, 1, 1, 21, 1, 1, 66, 1, 1, 3, 10, 1, 36, 1, 1, 15, 1, 1, 78, 1, 10, 3, 1, 1, 28, 1, 1, 3, 1, 1, 45, 91, 1, 3, 1

Offset: 1

Author

Leroy Quet, Feb 23 2006

Keywords

• nonn

Examples

			a(12) = 6 because the triangular numbers dividing 12 are 1, 3 and 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000217, A083312.

Programs

Maple

a:=proc(n) local P,j; P:={}: for j from 1 to n do if type(n/(j*(j+1)/2),integer)=true then P:=P union {j*(j+1)/2} else P:=P: fi od: P[nops(P)]; end: seq(a(n),n=1..105); # Emeric Deutsch, Mar 01 2006

Mathematica

With[{trnos=Accumulate[Range[100]]},Table[Last[Select[trnos,Divisible[ n,#]&]],{n,100}]] (* Harvey P. Dale, Nov 08 2011 *)
a[n_] := Module[{d = Divisors[2*n], nd, m}, nd = Floor[Length[d]/2]; m = Max[Intersection[d[[1 ;; nd]] + 1, d]]; m*(m-1)/2]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Jun 25 2025 *)

Formula

a(n) = A083312(n) * (A083312(n) + 1)/2.

Extensions

More terms from Emeric Deutsch, Mar 01 2006