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A324340 a(n) = A046692(A005940(1+n)), where A005940 is the Doudna sequence and A046692 is the Dirichlet inverse of sigma function.

%I A324340 #9 Feb 24 2019 17:52:04
%S A324340 1,-3,-4,2,-6,12,3,0,-8,18,24,-8,5,-9,0,0,-12,24,32,-12,48,-72,-18,0,
%T A324340 7,-15,-20,6,0,0,0,0,-14,36,48,-16,72,-96,-24,0,96,-144,-192,48,-40,
%U A324340 54,0,0,11,-21,-28,10,-42,60,15,0,0,0,0,0,0,0,0,0,-18,42,56,-24,84,-144,-36,0,112,-216,-288,64,-60,72,0,0,168,-288,-384,96,-576,576,144,0
%N A324340 a(n) = A046692(A005940(1+n)), where A005940 is the Doudna sequence and A046692 is the Dirichlet inverse of sigma function.
%H A324340 Antti Karttunen, <a href="/A324340/b324340.txt">Table of n, a(n) for n = 0..16383</a>
%H A324340 Antti Karttunen, <a href="/A324340/a324340.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A324340 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A324340 a(n) = A046692(A005940(1+n)).
%o A324340 (PARI) A324340(n) = { my(m1=1, p=2); while(n, if(!(n%2), p=nextprime(1+p); n>>=1, if(1==(n%4), m1 *= -(1+p), if(3==(n%8), m1 *= p, return(0))); while((n%2),n>>=1))); (m1); };
%o A324340 (PARI)
%o A324340 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A324340 A046692(n) = { my(f=factor(n)~); prod(i=1, #f, if(1==f[2,i], -(f[1,i]+1), if(2==f[2,i], f[1,i], 0))); };
%o A324340 A324340(n) = A046692(A005940(1+n));
%Y A324340 Cf. A005940, A046692.
%Y A324340 Cf. also A323915, A324335, A324336, A324339.
%K A324340 sign
%O A324340 0,2
%A A324340 _Antti Karttunen_, Feb 24 2019