A242370 - OEIS

%I #28 Jun 08 2014 09:02:07

%S 2,3,84,40,2,4,5,30,15,10,18,3,2,84,1907020800,7,42,840,280,14,168,

%T 58752,40,32640,2,96,4,8,540,54,3,9,117,84,135,252,20,5,238080,30,2,

%U 15,1120,10,10080,11,66,1320,198,33,132,22,264,528,44,392448,18,40,3

%N 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.

%C When p is prime T(p, 1) is equal to p.

%C When n and k are not coprime, T(n, k) = T(n/gcd(n, k), k/gcd(n,k)).

%C Next term T(12, 5) is <= 212569733376000 with sigma(x)/x = 65/12 and 65 == 5 mod 12.

%e T(2, 1) = 2 since sigma(2)/2 = 3/2 has denominator 2 and numerator 3 == 1(mod 2).

%e T(3, 1) = 3 since sigma(3)/3 = 4/3 has denominator 3 and numerator 4 == 1(mod 3).

%e T(3, 2) = 84 since sigma(84)/84 = 8/3 has denominator 3 and numerator 8 == 2(mod 3).

%e Triangle starts:

%e 2,

%e 3, 84,

%e 40, 2, 4,

%e 5, 30, 15, 10,

%e 18, 3, 2, 84, 1907020800,

%e 7, 42, 840, 280, 14, 168,

%e ...

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

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

%K nonn,tabl

%O 2,1

%A _Michel Marcus_, Jun 07 2014