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A175549 Number of triples (a, b, c) with gcd(a, b, c) = 1 and -n <= a,b,c <= n. 1
0, 26, 98, 290, 578, 1154, 1730, 2882, 4034, 5762, 7490, 10370, 12674, 16706, 20162, 24770, 29378, 36290, 41474, 50114, 57026, 66242, 74882, 87554, 96770, 111170, 123266, 138818, 152642, 172802, 186626, 209666, 228098, 251138, 271874, 299522 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
For n > 0, a(n) = 8*A090025(n) - 12*A018805(n) - 18.
a(n) = 2*n*(4*n^2 + 6*n + 3) - Sum_{j=2..n} a(floor(n/j)). - Chai Wah Wu, Mar 30 2021
MATHEMATICA
Table[If[n>0, 8 * Sum[MoebiusMu[k] * ((Floor[n/k] + 1)^3 - 1), {k, 1, n}] - 24 * Sum[EulerPhi[k], {k, 1, n}] - 6, 0], {n, 0, 35}] (* Indranil Ghosh, Mar 11 2017 *)
PROG
(PARI) a(n)=if(n>0, 8*sum(k=1, n, moebius(k)*((n\k+1)^3-1))-24*sum(k=1, n, eulerphi(k))-6)
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A175549(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
c += (j2-j)*A175549(k1)
j, k1 = j2, n//j2
return 4*n*(n - 1)*(2*n + 5)-c+26*(j-1)# Chai Wah Wu, Mar 30 2021
CROSSREFS
Sequence in context: A010014 A095796 A256645 * A159541 A144129 A026915
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Charles R Greathouse IV, Jul 19 2010
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)