A242370 Triangle read by rows: T(n, k) is the smallest x such that the denominator of sigma(x)/x is equal to n and the numerator of sigma(x)/x is congruent to k modulo n.

2, 3, 84, 40, 2, 4, 5, 30, 15, 10, 18, 3, 2, 84, 1907020800, 7, 42, 840, 280, 14, 168, 58752, 40, 32640, 2, 96, 4, 8, 540, 54, 3, 9, 117, 84, 135, 252, 20, 5, 238080, 30, 2, 15, 1120, 10, 10080, 11, 66, 1320, 198, 33, 132, 22, 264, 528, 44, 392448, 18, 40, 3

Offset: 2

Author

Michel Marcus, Jun 07 2014

Keywords

• nonn
• tabl

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.

Examples

			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,
...
		

Crossrefs

Cf. A017665 and A017666 (sigma(n)/n), A239578 and A162657 (similar sequences with numerators or denominators).

Programs

PARI

T(k, n) = {for (i=1, 10^10, ab = sigma(i)/i; if ((numerator(ab) % denominator(ab))/denominator(ab) == k/n, return (i)););}