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Triangle read by rows, inverse Möbius transform of a diagonalized matrix of A116477.
1

%I #15 Jun 27 2023 09:24:38

%S 1,1,2,1,0,4,1,2,0,5,1,0,0,0,9,1,2,4,0,0,7,1,0,0,0,0,0,15,1,2,0,5,0,0,

%T 0,12,1,0,4,0,0,0,0,0,18,1,2,0,0,9,0,0,0,0,15,1,0,0,0,0,0,0,0,0,0,28,

%U 1,2,4,5,0,7,0,0,0,0,0,16

%N Triangle read by rows, inverse Möbius transform of a diagonalized matrix of A116477.

%C For n-th row of the triangle, the inverse Möbius transform extracts A116477(k) such that k divides n; 0 otherwise.

%C Row sums = A006218: (1, 3, 5, 8, 10, 14, 16, ...).

%F Triangle read by rows, A051731 * (A116477 * 0^(n-k)); 1 <= k <= n.

%e First few rows of the triangle:

%e 1;

%e 1, 2;

%e 1, 0, 4;

%e 1, 2, 0, 5;

%e 1, 0, 0, 0, 9;

%e 1, 2, 4, 0, 0, 7;

%e 1, 0, 0, 0, 0, 0, 15;

%e 1, 2, 0, 5, 0, 0, 0, 12;

%e ...

%e Example: The divisors of 8 are (1, 2, 4, 8) so row 8 = (1, 2, 0, 5, 0, 0, 0, 12).

%Y Cf. A006218, A051731, A116477.

%K nonn,tabl

%O 1,3

%A _Gary W. Adamson_, Aug 29 2008

%E Diagonal sequence corrected to A116477 by _Georg Fischer_, Jun 27 2023