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A100613
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Number of elements in the set {(x,y): 1 <= x,y <= n, gcd(x,y) > 1}.
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7
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0, 1, 2, 5, 6, 13, 14, 21, 26, 37, 38, 53, 54, 69, 82, 97, 98, 121, 122, 145, 162, 185, 186, 217, 226, 253, 270, 301, 302, 345, 346, 377, 402, 437, 458, 505, 506, 545, 574, 621, 622, 681, 682, 729, 770, 817, 818, 881, 894, 953, 990, 1045, 1046, 1117, 1146, 1209
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OFFSET
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1,3
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LINKS
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FORMULA
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MATHEMATICA
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f[n_] := Table[ #^2 &[m], {m, 1, n + 1}] - FoldList[Plus, 1, 2 Array[EulerPhi, n, 2]] (* _Gregg K. Whisler_, Jun 25 2008 *)
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PROG
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(Haskell)
a100613 n = length [()| x <- [1..n], y <- [1..n], gcd x y > 1]
(PARI) a(n) = sum(i=1, n, sum(j=1, n, gcd(i, j)>1)); \\ Michel Marcus, Jan 30 2017
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
if n == 0:
return 0
c, j = 1, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 02 2004
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STATUS
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approved
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