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A145396 a(n) = Sum_{d|n} sigma(d) + 3*Sum_{2c|n} sigma(c). 1
1, 7, 5, 23, 7, 35, 9, 59, 18, 49, 13, 115, 15, 63, 35, 135, 19, 126, 21, 161, 45, 91, 25, 295, 38, 105, 58, 207, 31, 245, 33, 291, 65, 133, 63, 414, 39, 147, 75, 413, 43, 315, 45, 299, 126, 175, 49, 675, 66, 266, 95, 345, 55, 406, 91, 531, 105, 217, 61, 805, 63, 231, 162, 607 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..64.

J. S. Rutherford, The enumeration and symmetry-significant properties of derivative lattices, Act. Cryst. A48 (1992), 500-508. See Table 1, symmetry P2/m.

FORMULA

Dirichlet g.f. (1+3/2^s)*zeta(s-1)*(zeta(s))^2. Dirichlet convolution of [1,3,0,0,0,0,0,...] and A007429.

MAPLE

with(numtheory);

g:=proc(n)

local d, c, b, t0, t1, t2, t3;

t1:=divisors(n);

t0:=add( sigma(d), d in t1);

t2:=0;

for d in t1 do if d mod 2 = 0 then t2:=t2+sigma(d/2); fi; od:

t0+3*t2;

end;

[seq(g(n), n=1..100)];

# alternative

nmax := 100 :

L27 := [seq(i, i=1..nmax) ];

L := [1, 3, seq(0, i=1..nmax)] ;

MOBIUSi(%) ;

MOBIUSi(%) ;

DIRICHLET(%, L27) ; # R. J. Mathar, Sep 25 2017

MATHEMATICA

a[n_] := Sum[DivisorSigma[1, d] + 3 Boole[Mod[d, 2] == 0] DivisorSigma[1, d/2], {d, Divisors[n]}];

Array[a, 100] (* Jean-Fran├žois Alcover, Apr 04 2020 *)

CROSSREFS

Sequence in context: A166639 A078747 A213835 * A263825 A226661 A120404

Adjacent sequences:  A145393 A145394 A145395 * A145397 A145398 A145399

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Mar 13 2009

STATUS

approved

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Last modified May 18 19:29 EDT 2021. Contains 344002 sequences. (Running on oeis4.)