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A055155
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Sum_{k|n} [GCD(k,n/k)].
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2
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1, 2, 2, 4, 2, 4, 2, 6, 5, 4, 2, 8, 2, 4, 4, 10, 2, 10, 2, 8, 4, 4, 2, 12, 7, 4, 8, 8, 2, 8, 2, 14, 4, 4, 4, 20, 2, 4, 4, 12, 2, 8, 2, 8, 10, 4, 2, 20, 9, 14, 4, 8, 2, 16, 4, 12, 4, 4, 2, 16, 2, 4, 10, 22, 4, 8, 2, 8, 4, 8, 2, 30, 2, 4, 14, 8, 4, 8, 2, 20, 17, 4, 2, 16, 4, 4, 4, 12, 2, 20, 4, 8, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is odd iff n is odd square. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 27 2002
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FORMULA
| Multiplicative with a(p^e) = (p^(e/2)*(p+1)-2)/(p-1) for even e and a(p^e) = 2*(p^((e+1)/2)-1)/(p-1) for odd e. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 01 2001
Dirichlet g.f. (zeta(s))^2*zeta(2s-1)/zeta(2s); inverse Mobius transform of A000188. - R. J. Mathar, Feb 16 2011
Dirichlet convolution of A069290 and A008966. - R. J. Mathar, Oct 31 2011
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EXAMPLE
| a(9) = GCD(1,9) + GCD(3,3) + GCD(9,1) = 5, since 1, 3, 9 are the positive divisors of 9.
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CROSSREFS
| Cf. A057670.
Sequence in context: A169594 A124315 A101113 * A085191 A188581 A165872
Adjacent sequences: A055152 A055153 A055154 * A055156 A055157 A055158
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KEYWORD
| easy,nonn,mult
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AUTHOR
| Leroy Quet, Jul 02 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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