Search: id:A046692
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%I A046692
%S A046692 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,
%T A046692 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,
%U A046692 72,0,80,90,60,48,62,96,24,0,84,144,68,36,96,144,72,0,74,114,20,40,96,
               168
%V A046692 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,
%W A046692 -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,
%X A046692 72,0,80,90,-60,48,-62,96,-24,0,84,-144,-68,-36,96,-144,-72,0,-74,114,
               -20,-40,96,-168
%N A046692 Dirichlet inverse of sigma function (A000203).
%D A046692 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 39.
%D A046692 Feist, Andrew R., Fun With the Sigma-Function, unpub.
%F A046692 a(p) = -p-1, a(p^2) = p, a(p^k) = 0 for k > 2.
%e A046692 a(36) = a(2^2*3^2) = 2*3 = 6
%p A046692 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;
%o A046692 (PARI) a(n)=if(n<1,0,direuler(p=2,n,(1-X)*(1-p*X))[n]) (from R. Stephan)
%Y A046692 Cf. A000203.
%Y A046692 Sequence in context: A108127 A049277 A143052 this_sequence A166108 A045901 
               A098003
%Y A046692 Adjacent sequences: A046689 A046690 A046691 this_sequence A046693 A046694 
               A046695
%K A046692 easy,mult,sign,nice
%O A046692 1,2
%A A046692 Andrew R. Feist (arf22540(AT)cmsu2.cmsu.edu)
%E A046692 Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 13 2006

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