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A145398 a(n) = Sum_{d|n} sigma(d) - Sum_{2c|n} sigma(c) + 4*Sum_{4b|n} sigma(b). 2

%I

%S 1,3,5,11,7,15,9,31,18,21,13,55,15,27,35,75,19,54,21,77,45,39,25,155,

%T 38,45,58,99,31,105,33,167,65,57,63,198,39,63,75,217,43,135,45,143,

%U 126,75,49,375,66,114,95,165,55,174,91,279,105,93,61,385,63,99,162,355,105,195

%N a(n) = Sum_{d|n} sigma(d) - Sum_{2c|n} sigma(c) + 4*Sum_{4b|n} sigma(b).

%H J. S. Rutherford, <a href="https://dx.doi.org/10.1107/S0108767392000898">The enumeration and symmetry-significant properties of derivative lattices</a>, Act. Cryst. A48 (1992), 500-508. Table 1, symmetry C2/m.

%F 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.

%p 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

%Y Cf. A145378.

%K nonn,mult

%O 1,2

%A _N. J. A. Sloane_, Mar 13 2009

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Last modified June 20 15:52 EDT 2021. Contains 345165 sequences. (Running on oeis4.)