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A175549
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Number of triples (a, b, c) with gcd(a, b, c) = 1 and -n <= a,b,c <= n.
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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 2*n*(4*n^2 + 6*n + 3) - Sum_{j=2..n} a(floor(n/j)). - Chai Wah Wu, Mar 30 2021
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MATHEMATICA
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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 *)
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PROG
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(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)
if n == 0:
return 0
c, j = 0, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
return 4*n*(n - 1)*(2*n + 5)-c+26*(j-1)# Chai Wah Wu, Mar 30 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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