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A323403 Sum of sigma and its Dirichlet inverse: a(n) = A000203(n) + A046692(n).

%I A323403 #9 Jan 15 2019 18:42:50
%S A323403 2,0,0,9,0,24,0,15,16,36,0,20,0,48,48,31,0,30,0,30,64,72,0,60,36,84,
%T A323403 40,40,0,0,0,63,96,108,96,97,0,120,112,90,0,0,0,60,60,144,0,124,64,78,
%U A323403 144,70,0,120,144,120,160,180,0,216,0,192,80,127,168,0,0,90,192,0,0,195,0,228,104,100,192,0,0,186,121,252,0,288,216,264,240,180,0,288
%N A323403 Sum of sigma and its Dirichlet inverse: a(n) = A000203(n) + A046692(n).
%H A323403 Antti Karttunen, <a href="/A323403/b323403.txt">Table of n, a(n) for n = 1..16384</a>
%H A323403 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A323403 a(n) = A000203(n) + A046692(n).
%o A323403 (PARI)
%o A323403 up_to = 16384;
%o A323403 DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
%o A323403 A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
%o A323403 v046692 = DirInverse(vector(up_to,n,sigma(n)));
%o A323403 A046692(n) = v046692[n];
%o A323403 A323403(n) = (sigma(n)+A046692(n));
%Y A323403 Cf. A000203, A046692.
%Y A323403 Cf. also A319340, A322581, A323364, A323399, A323408.
%K A323403 nonn
%O A323403 1,1
%A A323403 _Antti Karttunen_, Jan 15 2019