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%I #13 Dec 06 2021 03:05:33
%S -1,0,0,2,-2,4,-2,10,8,4,-8,16,-8,8,8,38,-14,28,-14,20,16,4,-16,56,2,
%T 8,64,36,-26,32,-24,130,8,4,12,96,-32,8,16,76,-38,56,-38,32,72,12,-40,
%U 184,26,44,8,48,-46,164,-8,132,16,4,-56,112,-54,12,128,422,0,56,-62,44,24,72,-68,312,-66,8,88,60,0,80
%N a(n) = phi(A003961(n)) - 2*phi(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and phi is Euler totient function.
%C Möbius transform of A252748.
%H Antti Karttunen, <a href="/A349754/b349754.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A003972(n) - 2*A000010(n) = A337549(n) - A083254(n).
%F a(n) = A347100(n) - A000010(n).
%F a(n) = Sum_{d|n} A008683(n/d) * A252748(d).
%t f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := EulerPhi[s[n]] - 2*EulerPhi[n]; Array[a, 100] (* _Amiram Eldar_, Dec 04 2021 *)
%o (PARI)
%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A349754(n) = (eulerphi(A003961(n))-2*eulerphi(n));
%Y Cf. A000010, A003961, A003972, A008683, A083254, A252748, A337549, A347100.
%K sign
%O 1,4
%A _Antti Karttunen_, Dec 01 2021
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