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A164306
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Triangle read by rows: T(n, k) = k / gcd(k, n), 1 <= k <= n.
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8
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1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 4, 1, 1, 1, 1, 2, 5, 1, 1, 2, 3, 4, 5, 6, 1, 1, 1, 3, 1, 5, 3, 7, 1, 1, 2, 1, 4, 5, 2, 7, 8, 1, 1, 1, 3, 2, 1, 3, 7, 4, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 5, 1, 7, 2, 3, 5, 11, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1
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OFFSET
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1,5
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COMMENTS
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Also the gcd of the coefficients of the partition polynomials (called 'De Moivre polynomials' by O'Sullivan, see link, Theorem 4.1). - Peter Luschny, Sep 20 2022
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1,
1, 1,
1, 2, 1,
1, 1, 3, 1,
1, 2, 3, 4, 1,
1, 1, 1, 2, 5, 1,
1, 2, 3, 4, 5, 6, 1,
. . .
T(4,3) = 3 / gcd(3,4) = 3 / 1 = 3. (End)
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MAPLE
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seq(seq(k / igcd(n, k), k = 1..n), n = 1..13); # Peter Luschny, Sep 20 2022
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MATHEMATICA
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Flatten[Table[k/GCD[k, n], {n, 20}, {k, n}]] (* Harvey P. Dale, Jul 21 2013 *)
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PROG
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(PARI) for(n=0, 10, for(k=1, n, print1(k/gcd(k, n), ", "))) \\ G. C. Greubel, Sep 13 2017
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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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