

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.


0



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
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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: A037427 A042549 A182343 * A153228 A041401 A103013
Adjacent sequences: A242367 A242368 A242369 * A242371 A242372 A242373


KEYWORD

nonn,tabl


AUTHOR

Michel Marcus, Jun 07 2014


STATUS

approved



