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A087080
Number of elements in the coprime subsets of the integers 1 to n.
4
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
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