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 A287957 Table read by antidiagonals: T(n, k) = greatest common recursive divisor of n and k; n > 0 and k > 0. 3
 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 2, 1, 2, 5, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 7, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS We use the definition of recursive divisor given in A282446. More informally, the prime tower factorization of T(n, k) is the intersection of the prime tower factorizations of n and k (the prime tower factorization of a number is defined in A182318). This sequence has connections with the classical GCD (A003989). For any i > 0, j > 0 and k > 0: - T(i, j) = 1 iff gcd(i, j) = 1, - A007947(T(i, j)) = A007947(gcd(i, j)), - T(i, j) >= 1, - T(i, j) <= min(i, j), - T(i, j) <= gcd(i, j), - T(i, 1) = 1, - T(i, i) = i, - T(i, j) = T(j, i) (the sequence is commutative), - T(i, T(j, k)) = T(T(i, j), k) (the sequence is associative), - T(i, i*j) <= i, - if gcd(i, j) = 1 then T(i*j, k) = T(i, k) * T(j, k) (the sequence is multiplicative), - T(i, 2*i) = A259445(i). See also A287958 for the LCM equivalent. LINKS Rémy Sigrist, First 100 antidiagonals of array, flattened Rémy Sigrist, Illustration of the first terms EXAMPLE Table starts: n\k|    1   2   3   4   5   6   7   8   9   10 ---+----------------------------------------------- 1  |    1   1   1   1   1   1   1   1   1    1  ... 2  |    1   2   1   2   1   2   1   2   1    2  ... 3  |    1   1   3   1   1   3   1   1   3    1  ... 4  |    1   2   1   4   1   2   1   2   1    2  ... 5  |    1   1   1   1   5   1   1   1   1    5  ... 6  |    1   2   3   2   1   6   1   2   3    2  ... 7  |    1   1   1   1   1   1   7   1   1    1  ... 8  |    1   2   1   2   1   2   1   8   1    2  ... 9  |    1   1   3   1   1   3   1   1   9    1  ... 10 |    1   2   1   2   5   2   1   2   1   10  ... ... T(4, 8) = T(2^2, 2^3) = 2. PROG (PARI) T(n, k) = my (g=factor(gcd(n, k))); return (prod(i=1, #g~, g[i, 1]^T(valuation(n, g[i, 1]), valuation(k, g[i, 1])))) CROSSREFS Cf. A003989, A007947, A182318, A259445, A282446, A287958. Sequence in context: A329720 A140194 A159923 * A003989 A091255 A332013 Adjacent sequences:  A287954 A287955 A287956 * A287958 A287959 A287960 KEYWORD nonn,tabl,mult AUTHOR Rémy Sigrist, Jun 03 2017 STATUS approved

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Last modified May 17 05:13 EDT 2021. Contains 343965 sequences. (Running on oeis4.)