<a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

nonn,new

nonn

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

nonn,new

nonn

<a href="http://www.research.att.com/~njas/sequences/Sindx_PPer.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

Inverse: A056535.

nonn,new

nonn

Antti.Karttunen@iki.fi (karttu@megabaud.fi) 20. June 2000

Antti Karttunen Jun 20, 2000

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

1,2

<a href="http://www.research.att.com/~njas/sequences/Sindx_P.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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),...

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;

Inverse: A056535

nonn

Antti.Karttunen@iki.fi (karttu@megabaud.fi) 20. June 2000

approved