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A253473 a(n) = phi(c(n)) - tau(phi(c(n))), where c(n) is the n-th composite number.

%I A253473 #24 Oct 05 2019 11:46:55
%S A253473 0,0,1,2,1,1,2,4,4,2,4,6,6,4,14,6,12,6,4,11,14,11,16,6,12,16,11,6,14,
%T A253473 16,18,11,34,14,26,16,12,32,16,27,22,11,22,27,26,38,14,26,38,16,16,27,
%U A253473 32,27,48,16,26,46,32,16,57,34,48,32,16,60,38,48,42,60
%N A253473 a(n) = phi(c(n)) - tau(phi(c(n))), where c(n) is the n-th composite number.
%H A253473 Robert Israel, <a href="/A253473/b253473.txt">Table of n, a(n) for n = 1..10000</a>
%H A253473 J. Ziegenbalg, <a href="http://www.ziegenbalg.ph-karlsruhe.de/materialien-homepage-jzbg/materials-in-english/PhiTauSigma.pdf">Phi, Tau, Sigma in Elementary Number Theory</a>
%F A253473 a(n) = A049820(A073256(n)). - _Michel Marcus_, Jan 08 2015
%F A253473 a(n) = A000010(A002808(n)) - A000005(A000010(A002808(n))). - _Omar E. Pol_, Nov 20 2016
%e A253473 For n=1: c(1) = 4. phi(4) = 2. tau(2)= 2, thus a(1) = 2 - 2 = 0.
%e A253473 For n=3: c(3) = 8. phi(8) = 4. tau(4)= 3, thus a(3) = 4 - 3 = 1.
%e A253473 For n=20: c(20) = 32. phi(32) = 16. tau(16) = 5, thus a(20) = 16 - 5 = 11.
%p A253473 comps:= remove(isprime, [$2..1000]):
%p A253473 map( ((t->t) - numtheory:-tau)@numtheory:-phi, comps); # _Robert Israel_, Nov 20 2016
%t A253473 Composites := Select[Range[2, 10000], ! PrimeQ[#] &]; Composite[n_] := Last[Take[Composites, n]]; T[n_] := EulerPhi[n]; Table[T[Composite[n]] - DivisorSigma[0, T[Composite[n]]], {n, 200}]
%t A253473 EulerPhi[#]-DivisorSigma[0,EulerPhi[#]]&/@Select[Range[300],CompositeQ] (* _Harvey P. Dale_, Oct 05 2019 *)
%o A253473 (PARI) lista(nn) = {forcomposite(n=1, nn, ec = eulerphi(n); print1(ec - numdiv(ec), ", "););} \\ _Michel Marcus_, Jan 11 2015
%Y A253473 Cf. A000005, A000010, A002808.
%K A253473 nonn,easy
%O A253473 1,4
%A A253473 _Carlos Eduardo Olivieri_, Jan 02 2015
%E A253473 Name clarified by _Omar E. Pol_, Nov 20 2016