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A340362 a(n) = A005940(n) - A324106(n), where A324106(n) is multiplicative with a(p^e) = A005940(p^e).

%I A340362 #8 Jan 06 2021 17:48:23
%S A340362 0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,8,0,0,0,0,0,0,0,0,24,0,0,
%T A340362 -32,0,-12,0,0,0,-12,0,0,16,0,0,140,0,0,0,0,0,114,0,0,0,150,0,280,0,0,
%U A340362 48,0,0,180,0,-108,-64,0,0,-70,-24,0,0,0,0,18,0,140,-24,0,0,0,0,0,32,330,0,-60,0,0,280,300,0,632,0,300
%N A340362 a(n) = A005940(n) - A324106(n), where A324106(n) is multiplicative with a(p^e) = A005940(p^e).
%C A340362 It is conjectured that A070776 gives the positions of all zeros after the initial a(1) = 0. If that holds, then for all i, j: a(i) = a(j) => A340363(i) = A340363(j).
%H A340362 Antti Karttunen, <a href="/A340362/b340362.txt">Table of n, a(n) for n = 1..16384</a>
%o A340362 (PARI)
%o A340362 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A340362 A324106(n) = { my(f=factor(n)); prod(i=1, #f~, A005940(f[i,1]^f[i,2])); };
%o A340362 A340362(n) = (A005940(n)-A324106(n));
%Y A340362 Cf. A005940, A070776, A340364, A340365, A340366.
%Y A340362 Cf. also A305800, A340363.
%K A340362 sign
%O A340362 1,15
%A A340362 _Antti Karttunen_, Jan 06 2021