A289905 Square array T(n,k) (n>0, k>0) read by antidiagonals: if gcd(n,k)>1 then T(n,k)=-1, otherwise T(n,k) = the unique m such that A289815(m) = n and A289816(m) = k.

0, 1, 2, 3, -1, 6, 9, 5, 7, 18, 27, -1, -1, -1, 54, 4, 11, 15, 21, 19, 8, 81, -1, 33, -1, 57, -1, 162, 243, 29, -1, 45, 63, -1, 55, 486, 729, -1, 87, -1, -1, -1, 165, -1, 1458, 10, 83, 249, 99, 22, 17, 171, 489, 163, 20, 2187, -1, -1, -1, 135, -1, 189, -1, -1

Offset: 1

Author

Rémy Sigrist, Jul 14 2017

Keywords

• sign
• tabl
• base

Comments

This sequence, when restricted to the pairs of coprime numbers, is the inverse of the function n -> (A289815(n), A289816(n)).

If n and k are coprime, then the number of nonzero digits of the ternary representation of T(n,k) equals the number of distinct prime factors of n*k.

Examples

			The table begins:
x\y:    1       2       3       4       5       6       7       8   ...
1:      0       2       6       18      54      8       162     486 ...
2:      1       -1      7       -1      19      -1      55      -1  ...
3:      3       5       -1      21      57      -1      165     489 ...
4:      9       -1      15      -1      63      -1      171     -1  ...
5:      27      11      33      45      -1      17      189     513 ...
6:      4       -1      -1      -1      22      -1      58      -1  ...
7:      81      29      87      99      135     35      -1      567 ...
8:      243     -1      249     -1      297     -1      405     -1  ...
...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..5050
• Rémy Sigrist, PARI program for A289905

Crossrefs

Cf. A289815, A289816.

Programs

PARI

\\ See Links section.