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A324542 Möbius transform of A324118, where A324118(n) = A000593(A156552(n)).

%I A324542 #9 Mar 07 2019 23:28:50
%S A324542 0,1,1,3,1,4,1,4,3,11,1,3,1,16,4,16,1,5,1,4,11,46,1,8,3,82,4,27,1,10,
%T A324542 1,8,16,174,4,20,1,256,46,32,1,4,1,17,3,798,1,8,3,15,82,45,1,12,11,20,
%U A324542 174,1300,1,2,1,2734,4,72,16,27,1,125,256,8,1,20,1,4354,5,363,4,25,1,8,16,10926,1,53,46,20518,798,168,1,35,11,317
%N A324542 Möbius transform of A324118, where A324118(n) = A000593(A156552(n)).
%C A324542 The first three zeros after a(1) occur at n = 192, 288, 3645.
%C A324542 The first negative term is a(150) = -1. There are 184 negative terms among the first 4473 terms.
%H A324542 Antti Karttunen, <a href="/A324542/b324542.txt">Table of n, a(n) for n = 1..4473</a>
%H A324542 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324542 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324542 a(n) = Sum_{d|n} A008683(n/d) * A324118(d).
%o A324542 (PARI)
%o A324542 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A324542 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A324542 A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
%o A324542 A322993(n) = A156552(2*A246277(n));
%o A324542 memoA324118 = Map();
%o A324542 A324118(n) = if(1==n, 0, my(v); if(mapisdefined(memoA324118,n,&v), v, v=sigma(A322993(n)); mapput(memoA324118,n,v); (v)));
%o A324542 A324542(n) = sumdiv(n,d,moebius(n/d)*A324118(d));
%Y A324542 Cf. A000593, A008683, A156552, A324118, A324543.
%Y A324542 Cf. also A322993, A322994.
%K A324542 sign
%O A324542 1,4
%A A324542 _Antti Karttunen_, Mar 07 2019