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A130317 Smallest number having exactly n triangular divisors. 3
1, 3, 6, 36, 30, 90, 180, 210, 420, 630, 1890, 1260, 2520, 6930, 18480, 20790, 13860, 27720, 41580, 83160, 138600, 245700, 235620, 180180, 556920, 360360, 540540, 1670760, 1081080, 1413720, 2702700, 2162160, 6486480, 3063060, 8288280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

2*a(n) is smallest number having exactly n oblong divisors.

A007862(a(n)) = n and A007862(m) <> n for m < a(n).

LINKS

Ray Chandler and Donovan Johnson, Table of n, a(n) for n = 1..100 (first 58 terms from Ray Chandler)

FORMULA

a(n) = A088726(n-1)/2 for n>1. - Ray Chandler, Jun 24 2008

EXAMPLE

a(3)=6: A007862(6)=#{1,2*(2+1)/2,3*(3+1)/2}=3;

a(4)=36: A007862(36)=#{1,2*(2+1)/2,3*(3+1)/2,8*(8+1)/2}=4;

MATHEMATICA

t = {1, 3, 6, 36}; Do[k = 30; While[Count[Divisors[k], _?(IntegerQ[Sqrt[8 # + 1]] &)] != i, k += 30]; AppendTo[t, k], {i, 5, 30}]; t (* Jayanta Basu, Aug 12 2013 *)

CROSSREFS

Cf. A130279.

Sequence in context: A009197 A205336 A184390 * A019467 A106128 A119186

Adjacent sequences:  A130314 A130315 A130316 * A130318 A130319 A130320

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 23 2007

EXTENSIONS

Extended by Ray Chandler, Jun 24 2008

STATUS

approved

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)