A087087 Coprime sets of integers, each subset mapped onto a unique binary integer, values here shown in decimal.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 32, 33, 48, 49, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 96, 97, 112, 113, 128, 129, 132, 133, 144, 145, 148, 149, 192, 193, 196, 197

Offset

0,3

Comments

A coprime set of integers has no pair of elements for which (i,j)=0. Each element i in a subset contributes 2^(i-1) to the binary value for that subset. The integers missing from the sequence correspond to non-coprime subsets.

References

Alan Sutcliffe, Divisors and Common Factors in Sets of Integers, awaiting publication.

Links

Ivan Neretin, Table of n, a(n) for n = 0..3232 (all terms up to 2^20)

Example

a(11)=13 since the 11th coprime set counting from 0 is {4,3,1}, which maps onto 1101 binary = 13 decimal.

Mathematica

a = {}; Do[set = Select[Range[Log2[n] + 1], Reverse[IntegerDigits[n, 2]][[#]] == 1 &]; If[Union@Flatten@Outer[If[#1 == #2, 1, GCD[#1, #2]] &, set, set] == {1}, AppendTo[a, n]], {n, 200}]; a (* Ivan Neretin, Aug 14 2015 *)

Crossrefs

A087086 gives the corresponding values for the primitive sets of integers. A084422 gives the number of coprime subsets of the integers 1 to n.

Sequence in context: A048097 A130843 A350046 * A050742 A350572 A290387

Adjacent sequences: A087084 A087085 A087086 * A087088 A087089 A087090

Keyword

easy,nonn,base

Author

Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 16 2003

Status

approved