A056535 Mapping from the ordering by sum to the ordering by product of the ordered pairs. Inverse permutation to A056534.

1, 2, 3, 4, 7, 5, 6, 12, 13, 8, 9, 18, 22, 19, 10, 11, 25, 32, 33, 26, 14, 15, 31, 43, 48, 44, 34, 16, 17, 39, 55, 63, 64, 56, 40, 20, 21, 47, 68, 80, 86, 81, 69, 49, 23, 24, 54, 79, 98, 107, 108, 99, 82, 57, 27, 28, 62, 93, 116, 129, 136, 130, 117, 94, 65, 29, 30, 72, 106

Offset: 1

Author

Antti Karttunen, Jun 20 2000

Keywords

• nonn
• tabl

Comments

The last term of the each row r of the triangle is the first term of that row + (tau(r)-1).

As an array, T(n,k) is the index of the k-th term of A027750 whose value is n. - Michel Marcus, Oct 15 2015

Examples

			As a triangle, sequence begins:
1;
2, 3;
4, 7, 5;
6, 12, 13, 8;
9, 18, 22, 19, 10;
...
As an array, sequence begins:
1,   2,  4,  6,  9,  11,  15, ...
3,   7, 12, 18, 25,  31,  39, ...
5,  13, 22, 32, 43,  55,  68, ...
8,  19, 33, 48, 63,  80,  98, ...
10, 26, 44, 64, 86, 107, 129, ...
...
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

A056535[A000217[i]] = A056535[A000217[i-1]+1]+A000005[i]-1, for all i >= 1.

Left edge: A054519, Right edge: A006218.

Programs

Maple

Maple procedure nthmember given in A054426.

Mathematica

a[n_] := If[p = Position[A056534, n]; p != {}, p[[1, 1]], 0]; (* Jean-François Alcover, Aug 20 2013 *)

Formula

[seq(nthmember(j, A056534), j=1..105)];