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1, 2, 2, 6, 0, 3, 8, 4, 0, 4, 20, 0, 0, 0, 5, 12, 12, 6, 0, 0, 6, 42, 0, 0, 0, 0, 0, 7, 32, 16, 0, 8, 0, 0, 0, 8, 54, 0, 18, 0, 0, 0, 0, 0, 9, 40, 40, 0, 0, 10, 0, 0, 0, 0, 10, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 48, 24, 24, 24, 0, 12, 0, 0, 0, 0, 0, 12, 156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 84
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Natural number transform of A054523.
Row sums = n^2, left column = A002618
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LINKS
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FORMULA
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T(n,k) = Sum_{y=1..n} Sum_{x=1..n} [GCD(f(x,y), n) = k], where f(x,y) = x - y. - Mats Granvik, Oct 08 2023
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EXAMPLE
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First few rows of the triangle are:
1;
2, 2;
6, 0, 3;
8, 4, 0, 4;
20, 0, 0, 0, 5;
12, 12, 6, 0, 0, 6;
42, 0, 0, 0, 0, 0, 7;
...
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MAPLE
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A054523 := proc(n, k) if n mod k = 0 then numtheory[phi](n/k) ; else 0 ; fi ; end: A127649 := proc(n, k) A054523(n, k)*n ; end: for n from 1 to 20 do for k from 1 to n do printf("%d, ", A127649(n, k)) ; od: od: # R. J. Mathar, Nov 01 2007
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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