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A364575 a(n) = A364574(A005940(1+n)), where A364574 is the Dirichlet inverse of A005941 [the inverse permutation of A005940].

%I A364575 #14 Aug 06 2023 08:18:33
%S A364575 1,-2,-3,0,-5,6,2,0,-9,10,19,0,12,-4,0,0,-17,18,35,0,69,-38,-22,0,56,
%T A364575 -24,-64,0,-24,0,0,0,-33,34,67,0,133,-70,-42,0,265,-138,-339,0,-276,
%U A364575 44,8,0,240,-112,-288,0,-640,128,124,0,-336,48,176,0,48,0,0,0,-65,66,131,0,261,-134,-82,0,521,-266,-659,0
%N A364575 a(n) = A364574(A005940(1+n)), where A364574 is the Dirichlet inverse of A005941 [the inverse permutation of A005940].
%H A364575 Antti Karttunen, <a href="/A364575/b364575.txt">Table of n, a(n) for n = 0..16383</a>
%F A364575 a(n) = A364574(A005940(1+n)).
%o A364575 (PARI)
%o A364575 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A364575 A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After _David A. Corneth_'s program for A156552)
%o A364575 memoA364574 = Map();
%o A364575 A364574(n) = if(1==n,1,my(v); if(mapisdefined(memoA364574,n,&v), v, v = -sumdiv(n,d,if(d<n,A005941(n/d)*A364574(d),0)); mapput(memoA364574,n,v); (v)));
%o A364575 A364575(n) = A364574(A005940(1+n));
%Y A364575 Cf. A005940, A005941, A085405 (reduced modulo 2), A364574.
%Y A364575 Cf. also A324052, A324640 (scatter plots).
%K A364575 sign,look
%O A364575 0,2
%A A364575 _Antti Karttunen_, Aug 05 2023