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A130334
Smallest m>n such that the m-th and n-th triangular numbers are coprime.
5
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
1,1
LINKS
Eric Weisstein's World of Mathematics, Triangular Number
Eric Weisstein's World of Mathematics, Relatively Prime
FORMULA
a(n) > n+1 for n>1; a(n) > n+2 for n with n mod 3 = 0;
a(n) = n + A130335(n).
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 28 2007
STATUS
approved