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A077478 Rectangular array R by antidiagonals: R(i,j)=number of k that divide both i and j. +0
1
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)
OFFSET

1,5

COMMENT

Antidiagonal sums of R, alias row sums of T, are essentially A065608. Diagonal elements of R comprise A000203 (sums of divisors of n).

FORMULA

R=U*V, where U and V are the summatory matrices (A077049, A077051). The triangle T(n, k) formed by antidiagonals: T(n, k)=sigma(gcd(k, n+1-k)) for 1<=k<=n, where sigma(m)=A000203(m).

EXAMPLE

Northwest corner of R and top of T:

1.1.1.1.1.1..........1

1.2.1.2.1.2.........1.1

1.1.2.1.1.2........1.2.1

1.2.1.3.1.2.......1.1.1.1

1.1.1.1.2.1......1.2.2.2.1

1.2.2.2.1.4.....1.1.1.1.1.1

R(4,2)=2 since 1|2, 1|4, and 2|2, 2|4.

CROSSREFS

Cf. A051194, A077049, A077051.

Sequence in context: A025910 A002637 A134837 this_sequence A127836 A031262 A047072

Adjacent sequences: A077475 A077476 A077477 this_sequence A077479 A077480 A077481

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Nov 08 2002

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Last modified July 26 23:19 EDT 2008. Contains 142293 sequences.


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