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A077478 Rectangular array read R by antidiagonals: R(i,j) = number of integers k that divide both i and j (i >= 1, j >= 1). 2
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; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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, Nov 12 2007

If R(n) is the nxn Redheffer matrix (A143104) and Rt(n) is its transposed matrix, then this sequence seems to be formed by R(n)*Rt(n). - Enrique Pérez Herrero, Feb 21 2012

LINKS

Table of n, a(n) for n=1..105.

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)=tau(gcd(k, n+1-k)) for 1<=k<=n, where tau(m)=A000005(m). [Corrected by Leroy Quet, Apr 08 2009]

EXAMPLE

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.

CROSSREFS

Cf. A051194, A077049, A077051.

Cf. A051731, A065608.

Sequence in context: A025910 A002637 A166279 * A127836 A245618 A228053

Adjacent sequences:  A077475 A077476 A077477 * A077479 A077480 A077481

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Nov 08 2002

EXTENSIONS

Edited by N. J. A. Sloane, Jan 11 2009

STATUS

approved

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Last modified September 24 18:42 EDT 2017. Contains 292433 sequences.