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Search: id:A077478
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| A077478 |
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Rectangular array read R by antidiagonals: R(i,j) = number of integers k that divide both i and j (i >= 1, j >= 1). |
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+0
3
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| 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Antidiagonal sums of R, alias row sums of T, are essentially A065608. Diagonal elements of R comprise A000203 (sums of divisors of n).
Antidiagonals of an array formed by A051731 * A051731 (transposed). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 12 2007
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FORMULA
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R=U*V, where U and V are the summatory matrices (A077049, A077051). The triangle T(n, k) formed by antidiagonals: T(n, k)=tau(gcd(k, n+1-k)) for 1<=k<=n, where tau(m)=A000005(m). [Corrected by Leroy Quet, Apr 08 2009]
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EXAMPLE
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First few rows of the array R are:
1, 1, 1, 1, 1, 1, 1,...
1, 2, 1, 2, 1, 2, 1,...
1, 1, 2, 1, 1, 2, 1,...
1, 2, 1, 3, 1, 2, 1,...
1, 1, 1, 1, 2, 1, 1,...
1, 2, 2, 2, 1, 4, 1,...
...
First few rows of the triangle T are:
1;
1, 1;
1, 2, 1;
1, 1, 1, 1;
1, 2, 2, 2, 1;
1, 1, 1, 1, 1, 1;
1, 2, 1, 3, 1, 3, 1;
1, 1, 2, 1, 1, 2, 1, 1;
1, 2, 1, 2, 2, 2, 1, 2, 1;
1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1;
...
R(4,2)=2 since 1|2, 1|4 and 2|2, 2|4.
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CROSSREFS
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Cf. A051194, A077049, A077051.
Cf. A051731, A065608.
Sequence in context: A025910 A002637 A166279 this_sequence A127836 A031262 A047072
Adjacent sequences: A077475 A077476 A077477 this_sequence A077479 A077480 A077481
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Nov 08 2002
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 11 2009
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