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A324335 a(n) = A323363(A005940(1+n)), where A005940 is the Doudna sequence and A323363 is the Dirichlet inverse of Dedekind's psi.

%I A324335 #10 Feb 24 2019 01:59:18
%S A324335 1,-3,-4,3,-6,12,4,-3,-8,18,24,-12,6,-12,-4,3,-12,24,32,-18,48,-72,
%T A324335 -24,12,8,-18,-24,12,-6,12,4,-3,-14,36,48,-24,72,-96,-32,18,96,-144,
%U A324335 -192,72,-48,72,24,-12,12,-24,-32,18,-48,72,24,-12,-8,18,24,-12,6,-12,-4,3,-18,42,56,-36,84,-144,-48,24,112,-216,-288,96,-72,96,32,-18
%N A324335 a(n) = A323363(A005940(1+n)), where A005940 is the Doudna sequence and A323363 is the Dirichlet inverse of Dedekind's psi.
%H A324335 Antti Karttunen, <a href="/A324335/b324335.txt">Table of n, a(n) for n = 0..16383</a>
%H A324335 Antti Karttunen, <a href="/A324335/a324335.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A324335 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A324335 a(n) = A323363(A005940(1+n)).
%o A324335 (PARI)
%o A324335 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A324335 A001615(n) = (n * sumdivmult(n, d, issquarefree(d)/d)); \\ From A001615
%o A324335 memoA323363 = Map();
%o A324335 A323363(n) = if(1==n,1,my(v); if(mapisdefined(memoA323363,n,&v), v, v = -sumdiv(n,d,if(d<n,A001615(n/d)*A323363(d),0)); mapput(memoA323363,n,v); (v)));
%o A324335 A324335(n) = A323363(A005940(1+n));
%Y A324335 Cf. A001615, A005940, A323363, A323915, A324336.
%K A324335 sign
%O A324335 0,2
%A A324335 _Antti Karttunen_, Feb 23 2019