A130334 Smallest m>n such that the m-th and n-th triangular numbers are coprime.

2, 4, 10, 6, 7, 10, 9, 10, 13, 12, 13, 22, 15, 16, 22, 18, 19, 22, 21, 22, 25, 24, 25, 37, 27, 28, 37, 30, 31, 37, 33, 34, 37, 36, 37, 46, 39, 40, 46, 42, 43, 46, 45, 46, 52, 48, 49, 58, 51, 52, 58, 54, 55, 58, 57, 58, 61, 60, 61, 73, 63, 64, 73, 66, 67, 70, 69, 70, 73, 72, 73

Offset: 1

Author

Reinhard Zumkeller, May 28 2007

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Triangular Number
• Eric Weisstein's World of Mathematics, Relatively Prime

Crossrefs

Cf. A000217, A026741, A109007, A130335.

Programs

Python

from math import gcd
def A130334(n):
    k, Tn, Tm = n+1, n*(n+1)//2, (n+1)*(n+2)//2
    while gcd(Tn,Tm) != 1:
        k += 1
        Tm += k
    return k # Chai Wah Wu, Sep 16 2021

Formula

a(n) > n+1 for n>1; a(n) > n+2 for n with n mod 3 = 0;

a(n) = n + A130335(n).