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 A130836 Array read by antidiagonals: d(m,n) (m>=1, n>=1) = multiplicative distance between m and n. 3
 0, 1, 1, 1, 0, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 2, 0, 2, 1, 1, 3, 2, 1, 3, 3, 1, 2, 3, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 3, 4, 3, 3, 3, 3, 4, 3, 2, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 1, 3, 2, 3, 4, 4, 3, 3, 4, 4, 3, 2, 3, 1, 2, 2, 2, 3, 3, 0, 3, 3, 2, 2, 2, 1, 2, 2, 2, 3, 1, 2, 4, 4, 2, 1, 3, 2, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS If m = p_1^e_1 * p_2^e_2 * ... * p_k^e^k, n = p_1^f_1 * p_2^f_2 * ... * p_k^f^k we define d(m, n) = Sum[ Abs[e_i - f_i], {i, 1, k}] to be the multiplicative distance between m and n (see A130849). LINKS D. Dominici, An Arithmetic Metric, arXiv:0906.0632 FORMULA a(n,m) = A127185(n,m). - R. J. Mathar, Oct 17 2007 EXAMPLE Array begins: 0 1 1 2 1 2 1 3 ... 1 0 2 1 2 1 2 2 ... 1 2 0 3 2 1 2 4 ... 2 1 3 0 3 2 3 1 ... ... MAPLE A001222 := proc(n) numtheory[bigomega](n) ; end: A127185 := proc(n, m) local g ; g := gcd(n, m) ; RETURN(A001222(n/g)+A001222(m/g)) ; end: A130836 := proc(n, m) A127185(n, m) ; end: for d from 1 to 17 do for n from 1 to d do printf("%d, ", A130836(n, d-n+1)) ; od: od: - R. J. Mathar, Oct 17 2007 CROSSREFS Half of antidiagonal sums gives A130849. First row is A001222. Sequence in context: A174344 A049241 A101080 * A161385 A152907 A078786 Adjacent sequences:  A130833 A130834 A130835 * A130837 A130838 A130839 KEYWORD nonn,tabl,easy AUTHOR N. J. A. Sloane, Sep 28 2007 EXTENSIONS More terms from R. J. Mathar, Oct 17 2007 STATUS approved

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