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

1,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000217, A083312.

Sequence in context: A324284 A300791 A069972 * A088439 A162315 A109446

Adjacent sequences: A115014 A115015 A115016 * A115018 A115019 A115020

Keyword

nonn

Author

Leroy Quet, Feb 23 2006

Extensions

More terms from Emeric Deutsch, Mar 01 2006

Status

approved