OFFSET
2,1
COMMENTS
When p is prime T(p, 1) is equal to p.
When n and k are not coprime, T(n, k) = T(n/gcd(n, k), k/gcd(n,k)).
Next term T(12, 5) is <= 212569733376000 with sigma(x)/x = 65/12 and 65 == 5 mod 12.
EXAMPLE
T(2, 1) = 2 since sigma(2)/2 = 3/2 has denominator 2 and numerator 3 == 1(mod 2).
T(3, 1) = 3 since sigma(3)/3 = 4/3 has denominator 3 and numerator 4 == 1(mod 3).
T(3, 2) = 84 since sigma(84)/84 = 8/3 has denominator 3 and numerator 8 == 2(mod 3).
Triangle starts:
2,
3, 84,
40, 2, 4,
5, 30, 15, 10,
18, 3, 2, 84, 1907020800,
7, 42, 840, 280, 14, 168,
...
PROG
(PARI) T(k, n) = {for (i=1, 10^10, ab = sigma(i)/i; if ((numerator(ab) % denominator(ab))/denominator(ab) == k/n, return (i)); ); }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Jun 07 2014
STATUS
approved