A144531 Triangle read by rows: T(m,n) = the smallest positive integer that has a factor in common with both m and n (2 <= n <= m).

2, 6, 3, 2, 6, 2, 10, 15, 10, 5, 2, 3, 2, 10, 2, 14, 21, 14, 35, 14, 7, 2, 6, 2, 10, 2, 14, 2, 6, 3, 6, 15, 3, 21, 6, 3, 2, 6, 2, 5, 2, 14, 2, 6, 2, 22, 33, 22, 55, 22, 77, 22, 33, 22, 11, 2, 3, 2, 10, 2, 14, 2, 3, 2, 22, 2, 26, 39, 26, 65, 26, 91, 26, 39, 26, 143, 26, 13, 2, 6

Offset

2,1

Comments

Diagonal of triangle is A020639. - Michel Marcus, Aug 29 2013

Links

Diana Mecum, Table of n, a(n) for n=2,...,4951

Formula

If gcd(m,n) = 1 then T(m,n) = smallest prime factor of m times smallest prime factor of n, if gcd(m,n) > 1 then T(m,n) = min { smallest prime factor of m times smallest prime factor of n, smallest prime factor of gcd(m,n) }.

Example

Triangle begins:
2
6 3
2 6 2
10 15 10 5
2 3 2 10 2
...

Prog

(PARI) t(m, n) = {ff = factor(m)[1, 1] * factor(n)[1, 1]; if ((g = gcd(m, n)) == 1, t = ff, t = min(ff, factor(g)[1, 1]); ); t; } - Michel Marcus, Aug 29 2013

Crossrefs

A141327 gives the analogous doubly-infinite array.

Sequence in context: A056113 A251755 A128203 * A086357 A138054 A297927

Adjacent sequences: A144528 A144529 A144530 * A144532 A144533 A144534

Keyword

nonn,tabl

Author

N. J. A. Sloane, Dec 28 2008, based on emails from Leroy Quet and Diana Mecum

Status

approved