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A130836
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Array read by antidiagonals: d(m,n) (m>=1, n>=1) = multiplicative distance between m and n.
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3
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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
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OFFSET
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1,7
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=1..105.
D. Dominici, An Arithmetic Metric, arXiv:0906.0632
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FORMULA
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a(n,m) = A127185(n,m). - R. J. Mathar, Oct 17 2007
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EXAMPLE
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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 ...
...
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MAPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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N. J. A. Sloane, Sep 28 2007
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EXTENSIONS
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More terms from R. J. Mathar, Oct 17 2007
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STATUS
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approved
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