A056534 Mapping from the ordering by product (A027750, A056538) to the ordering by sum (A002260, A004736) of ordered pairs (a,b), a>=1, b>=1.

1, 2, 3, 4, 6, 7, 5, 10, 11, 15, 16, 8, 9, 21, 22, 28, 29, 12, 14, 36, 37, 13, 45, 46, 17, 20, 55, 56, 66, 67, 23, 18, 19, 27, 78, 79, 91, 92, 30, 35, 105, 106, 24, 26, 120, 121, 38, 25, 44, 136, 137, 153, 154, 47, 31, 34, 54, 171, 172, 190, 191, 57, 32, 33, 65, 210, 211, 39

Offset: 1

Author

Antti Karttunen, Jun 20 2000

Keywords

• nonn

Examples

			The "ordering by sum": (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),(1,4),(2,3),(3,2),(4,1),...
The "ordering by product": (1,1),(1,2),(2,1),(1,3),(3,1),(1,4),(2,2),(4,1),(1,5),(5,1),...
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A056535.

Programs

Maple

ordered_pair_perm := proc(upto_n) local a,i,j; a := []; for i from 1 to upto_n do for j in sort(divisors(i)) do a := [op(a),binomial(((i/j) + j - 1),2)+j]; od; od; RETURN(a); end;

Mathematica

max = 21; A056534 = {}; For[i = 1, i <= max, i++, Do[ AppendTo[ A056534, Binomial[i/j + j - 1, 2] + j], {j, Divisors[i]}]]; A056534 (* Jean-François Alcover, Oct 05 2012, after Maple *)