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

1,1

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A350991 A084260 A076983 * A003674 A211895 A240986

Adjacent sequences: A068081 A068082 A068083 * A068085 A068086 A068087

Keyword

easy,nonn

Author

Amarnath Murthy, Feb 18 2002

Extensions

Edited by Dean Hickerson, Feb 20 2002

Status

approved