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A006579
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Sum of GCD(n,k) for k = 1 to n-1.
(Formerly M0941)
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10
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0, 1, 2, 4, 4, 9, 6, 12, 12, 17, 10, 28, 12, 25, 30, 32, 16, 45, 18, 52, 44, 41, 22, 76, 40, 49, 54, 76, 28, 105, 30, 80, 72, 65, 82, 132, 36, 73, 86, 140, 40, 153, 42, 124, 144, 89, 46, 192, 84, 145, 114, 148, 52, 189, 134, 204, 128, 113, 58, 300, 60, 121, 210, 192
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..2000
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FORMULA
| a(p) = p-1 for a prime p.
a(n) = A018804(n)-n = Sum_{ d divides n } (d-1)*phi(n/d). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 04 2002
a(n+2)=sum{k=0..n, gcd(n-k+1, k+1)}=-sum{k=0..4n+2, gcd(4n-k+3, k+1)(-1)^k/4} - Paul Barry (pbarry(AT)wit.ie), May 03 2005
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EXAMPLE
| a(12) = GCD(12,1) + GCD(12,2) + ... GCD(12,11) = 1+2+3+4+1+6+1+4+3+2+1 = 28.
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MATHEMATICA
| f[n_] := Sum[ GCD[n, k], {k, 1, n - 1}]; Table[ f[n], {n, 1, 60}]
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PROG
| (PARI) A006579(n) = sum(k=1, n-1, gcd(n, k)) [From Michael B. Porter (michael_b_porter(AT)yahoo.com), Feb 23 2010]
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CROSSREFS
| Antidiagonal sums of array A003989.
Sequence in context: A096189 A010464 A187209 * A195727 A039887 A114215
Adjacent sequences: A006576 A006577 A006578 * A006580 A006581 A006582
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KEYWORD
| nonn
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AUTHOR
| Marc LeBrun (mlb(AT)well.com)
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 04 2002
Corrected by Ron Lalonde (ronronronlalonde(AT)hotmail.com), Oct 24 2002
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