A130317 Smallest number having exactly n triangular divisors.

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

Offset: 1

Author

Reinhard Zumkeller, May 23 2007

Keywords

• nonn

Comments

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

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

Examples

			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;
		

Links

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

Crossrefs

Cf. A007862, A088726, A130279.

Programs

PARI

a(n) = my(k=1); while (sumdiv(k, d, ispolygonal(d,3)) != n, k++); k; \\ Michel Marcus, Jan 14 2022

Formula

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

Extensions

Extended by Ray Chandler, Jun 24 2008