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A145398
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a(n) = Sum_{d|n} sigma(d) - Sum_{2c|n} sigma(c) + 4*Sum_{4b|n} sigma(b).
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0
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1, 3, 5, 11, 7, 15, 9, 31, 18, 21, 13, 55, 15, 27, 35, 75, 19, 54, 21, 77, 45, 39, 25, 155, 38, 45, 58, 99, 31, 105, 33, 167, 65, 57, 63, 198, 39, 63, 75, 217, 43, 135, 45, 143, 126, 75, 49, 375, 66, 114, 95, 165, 55, 174, 91, 279, 105, 93, 61, 385, 63, 99, 162, 355, 105, 195
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OFFSET
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1,2
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REFERENCES
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J. S. Rutherford, The enumeration and symmetry-significant properties of derivative lattices, Acta Cryst. A48 (1992), 500-508. Table 1, symmetry C2/m.
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LINKS
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Table of n, a(n) for n=1..66.
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FORMULA
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Dirichlet g.f. (1-1/2^s+4/4^s)*(zeta(s))^2*zeta(s-1), Dirichlet convolution of [1,-1,0,4,0,0...] with A007429.
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MAPLE
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read("transforms") ; s1 := [1, -1, 0, 4, seq(0, n=1..40)] ; s2 := [seq(add(sigma(d), d=divisors(n)), n=1..40)] ; DIRICHLET(s1, s2) ; # R. J. Mathar, Feb 07 2011
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CROSSREFS
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Cf. A145378.
Sequence in context: A154561 A073653 A225487 * A087322 A094747 A129738
Adjacent sequences: A145395 A145396 A145397 * A145399 A145400 A145401
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane, Mar 13 2009
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STATUS
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approved
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