A134866 - OEIS

%I #18 Dec 20 2022 11:50:18

%S 1,1,1,1,3,1,1,1,1,1,1,3,4,3,1,1,1,1,1,1,1,1,3,1,7,1,3,1,1,1,4,1,1,4,

%T 1,1,1,3,1,3,6,3,1,3,1,1,1,1,1,1,1,1,1,1,1,1,3,4,7,1,12,1,7,4,3,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,3,1,3,1,3,8,3,1,3,1,3,1

%N Table read by antidiagonals: T(n,k) = sigma(gcd(n,k)).

%C Previous name was: Triangle, antidiagonals of an array formed by A051731 * A127093 (transform).

%C Row sums give A094471.

%H Michael De Vlieger, <a href="/A134866/b134866.txt">Table of n, a(n) for n = 1..11325</a> (rows n = 1..150, flattened)

%F T(n,k) = A000203(A050873(n,k)). - _Michel Marcus_, Dec 19 2022

%e First few rows of the array:

%e   1, 1, 1, 1, 1, 1, 1, ...

%e   1, 3, 1, 3, 1, 3, 1, ...

%e   1, 1, 4, 1, 1, 4, 1, ...

%e   1, 3, 1, 7, 1, 3, 1, ...

%e   1, 1, 1, 1, 6, 1, 1, ...

%e   ...

%e First antidiagonals:

%e   1;

%e   1, 1;

%e   1, 3, 1;

%e   1, 1, 1, 1;

%e   1, 3, 4, 3, 1;

%e   1, 1, 1, 1, 1, 1;

%e   1, 3, 1, 7, 1, 3, 1;

%e   1, 1, 4, 1, 1, 4, 1, 1;

%e   1, 3, 1, 3, 6, 3, 1, 3, 1;

%e   ...

%t Table[DivisorSigma[1, GCD[#, k]] &[n - k + 1], {n, 13}, {k, n}] // Flatten (* _Michael De Vlieger_, Dec 19 2022 *)

%o (PARI) T(n, k) = sigma(gcd(n, k)); \\ _Michel Marcus_, Dec 19 2022

%Y Cf. A051731, A127093, A094471, A132442.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_, Nov 14 2007

%E New name and data corrected by _Michel Marcus_, Dec 19 2022