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

0,3

Comments

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

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.

Formula

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

Example

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

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.

Sequence in context: A107384 A205596 A092446 * A200276 A168081 A340399

Adjacent sequences: A087074 A087075 A087076 * A087078 A087079 A087080

Keyword

nonn

Author

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

Extensions

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

Status

approved