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

2,1

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.

Links

Table of n, a(n) for n=2..60.

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

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

Sequence in context: A042549 A365291 A182343 * A153228 A041401 A103013

Adjacent sequences: A242367 A242368 A242369 * A242371 A242372 A242373

Keyword

nonn,tabl

Author

Michel Marcus, Jun 07 2014

Status

approved