|
|
|
|
1, 2, 3, 5, 6, 9, 11, 14, 16, 21, 23, 29, 32, 36, 40, 48, 51, 60, 64, 70, 75, 86, 90, 100, 106, 115, 121, 135, 139, 154, 162, 172, 180, 192, 198, 216, 225, 237, 245, 265, 271, 292, 302, 314, 325, 348, 356, 377, 387, 403, 415, 441, 450, 470, 482
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
COMMENTS
|
a(n) = |{(x,y) : 1 <= x <= y <= n, x + y <= n, 1 = gcd(x,y)}| = |{(x,y) : 1 <= x <= y <= n, x + y > n, 1 = gcd(x,y)}|. - Steve Butler, Mar 31 2006
Brousseau proved that if the starting numbers of a generalized Fibonacci sequence are <= n (for n > 1) then the number of such sequences with relatively prime successive terms is a(n). - Amiram Eldar, Mar 31 2017
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 1/2 + Sum_{i<j<=n, gcd(i, j) = 1} i/j. - Joseph Wheat, Feb 22 2018
|
|
MAPLE
|
a:=n->sum(numtheory[phi](k), k=1..n): seq(a(n)/2, n=2..60); # Muniru A Asiru, Mar 05 2018
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) a(n) = sum(k=1, n, eulerphi(k))/2; \\ Michel Marcus, Apr 01 2017
(GAP) List([2..60], n->Sum([1..n], k->Phi(k)/2)); # Muniru A Asiru, Mar 05 2018
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
if n == 0:
return 0
c, j = 0, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|