A087080 Number of elements in the coprime subsets of the integers 1 to n.

0, 1, 4, 12, 20, 52, 60, 148, 196, 300, 332, 780, 828, 1904, 2080, 2348, 2812, 6352, 6608, 14736, 15632, 17456, 18640, 41152, 42432, 60912, 64800, 80928, 85408, 186304, 187584, 406400, 457344, 497472, 523456, 585280, 596288, 1284224, 1348032, 1457792, 1495424

Offset

0,3

Comments

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

References

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

Links

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

Example

a(4)=20 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 these contain 20 elements.

Prog

(PARI) iscoprime(v) = {local(i); for (i=1, #v-1, for (j=i+1, #v, if (gcd(v[i], v[j]) != 1, return (0)); ); ); return (1); }
a(n) = {sn = vector(n, i, i); pset = vector(1<<#sn, i, vecextract(sn, i-1)); nb = 0; for (i=1, #pset, if (iscoprime(pset[i]), nb += #pset[i]); ); return (nb); } \\ Michel Marcus, Jul 12 2013

Crossrefs

A087077 gives the number of elements in the primitive subsets. A084422 gives the number coprime subsets. A087081 gives the sum of the elements in coprime subsets.

Sequence in context: A316299 A301231 A151914 * A134253 A115106 A365686

Adjacent sequences: A087077 A087078 A087079 * A087081 A087082 A087083

Keyword

nonn

Author

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

Extensions

Terms a(38) and beyond from Fausto A. C. Cariboni, Oct 20 2020

Status

approved