A087078 -id:A087078 - cp's OEIS frontend

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

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

nonn

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

			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

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

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

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.

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

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

A087081 Sum of the elements in the coprime subsets of the integers 1 to n.

Original entry on oeis.org

0, 1, 6, 24, 48, 156, 192, 580, 836, 1444, 1660, 4596, 4980, 13184, 14768, 17308, 21756, 55888, 58768, 146416, 157552, 181008, 196304, 481664, 500096, 765648, 825152, 1073920, 1148288, 2745728, 2768768, 6505728, 7453952, 8233792, 8736960, 9984832, 10208064

Offset: 0

Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 12 2003

nonn

A coprime set of integers has (m,n)=1 for each pair of integers in the set.

			a(4)=48 since the 12 coprime subsets of (1,2,3,4) are ( ) (1) (2) (3) (4) (1,2) (1,3) (1,4) (2,3) (3,4) (1,2,3) (1,3 4) and the sum of the elements is 48.

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

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..120

A087078 gives the sum of the elements in the primitive subsets. A084422 gives the number coprime subsets. A087080 gives the number of elements in coprime subsets.

Terms a(35) and beyond from Fausto A. C. Cariboni, Oct 20 2020

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Formula

Extensions