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

Author

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

Keywords

• easy
• nonn
• base

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.

Examples

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

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)

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.

Programs

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 *)