A068084 Smallest triangular number which is a multiple (>1) of the n-th triangular number.

3, 6, 36, 120, 45, 105, 1176, 2016, 630, 990, 528, 780, 3003, 210, 3240, 32640, 9180, 11628, 2850, 630, 3003, 26565, 16836, 20100, 44850, 52650, 17766, 20706, 10440, 12090, 461280, 61776, 11781, 3570, 25200, 43956, 221445, 30381, 5460, 189420

Offset: 1

Author

Amarnath Murthy, Feb 18 2002

Keywords

• easy
• nonn

Examples

			The fifth triangular number is 15; the next triangular number that's divisible by 15 is 45, so a(5)=45.
		

Links

• Zak Seidov and Chai Wah Wu, Table of n, a(n) for n = 1..10000 n = 1..1000 from Zak Seidov

Programs

Mathematica

a[n_] := For[k=n+1, True, k++, If[Mod[k(k+1), n(n+1)]==0, Return[k(k+1)/2]]]

Python

from _future_ import division
def A068084(n):
    u,v,t = 4*(n+1),(2*(n+1))**2-1,4*n*(n+1)
    while True:
        if not v % t:
            return v//8
        v += u+1
        u += 2 # Chai Wah Wu, Jan 13 2016

Extensions

Edited by Dean Hickerson, Feb 20 2002