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A046692 Dirichlet inverse of sigma function (A000203). 3
1, -3, -4, 2, -6, 12, -8, 0, 3, 18, -12, -8, -14, 24, 24, 0, -18, -9, -20, -12, 32, 36, -24, 0, 5, 42, 0, -16, -30, -72, -32, 0, 48, 54, 48, 6, -38, 60, 56, 0, -42, -96, -44, -24, -18, 72, -48, 0, 7, -15, 72, -28, -54, 0, 72, 0, 80, 90, -60, 48, -62, 96, -24, 0, 84, -144, -68, -36, 96, -144, -72, 0, -74, 114, -20, -40, 96, -168 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 39.

Feist, Andrew R., Fun With the Sigma-Function, unpub.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

a(p) = -p-1, a(p^2) = p, a(p^k) = 0 for k > 2.

EXAMPLE

a(36) = a(2^2*3^2) = 2*3 = 6

MAPLE

t := 1; a := proc(n, t) local t1, d; t1 := 0; for d from 1 to n do if n mod d = 0 then t1 := t1+d^t*mobius(d)*mobius(n/d); fi; od; t1; end;

MATHEMATICA

a[n_] := (k = 0; Do[If[Mod[n, d] == 0, k = k + d*MoebiusMu[d]*MoebiusMu[n/d]], {d, 1, n}]; k); Table[a[n], {n, 1, 78}](* Jean-Fran├žois Alcover, Oct 13 2011, after Maple *)

PROG

(PARI) a(n)=if(n<1, 0, direuler(p=2, n, (1-X)*(1-p*X))[n]) /* Ralf Stephan */

CROSSREFS

Cf. A000203.

Sequence in context: A143052 A243256 A269868 * A205769 A166108 A255768

Adjacent sequences:  A046689 A046690 A046691 * A046693 A046694 A046695

KEYWORD

easy,mult,sign,nice

AUTHOR

Andrew R. Feist (arf22540(AT)cmsu2.cmsu.edu)

EXTENSIONS

Corrected by T. D. Noe, Nov 13 2006

STATUS

approved

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Last modified April 30 08:33 EDT 2017. Contains 285645 sequences.