A087077 Total number of elements in all primitive subsets of the integers 1 to n.

0, 1, 2, 5, 8, 21, 29, 73, 105, 193, 288, 677, 853, 1957, 2961, 4913, 6809, 15145, 19605, 43105, 57889, 98849, 151457, 327505, 397825, 784945, 1201189, 2009229, 2772729, 5901185, 7364945, 15609825, 21206049, 36440033, 55602033, 105010513, 127336513, 267374561

Offset: 0

Author

Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 10 2003

Keywords

• nonn

Comments

A primitive set has no element that divides another element in the same set.

Examples

			a(4)=8 since the primitive subsets of (1,2,3,4) are ( ) (1) (2) (3) (4) (2,3) (3,4) and these contain eight elements
		

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, New York, (1994).

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..75
• Eric Weisstein's World of Mathematics, Primitive Sequence.

Crossrefs

A051026 gives the number of primitive subsets. A087078 gives the sum of the elements of the primitive subsets. A087080 gives the number elements in the coprime subsets.

Cf. A355145.

Formula

a(n) = Sum_{k=1..ceiling(n/2)} k * A355145(n,k). - Alois P. Heinz, Jun 27 2022

Extensions

Terms a(34)-a(37) from Fausto A. C. Cariboni, Feb 02 2022