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A289905
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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.
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2
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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 ...
...
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PROG
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See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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