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A160620 a(n) = Sum_{d|n} phi(n/d)^2*2^d.

%I A160620 #12 Jun 25 2021 01:52:11
%S A160620 0,2,6,16,28,64,96,200,320,616,1152,2248,4304,8480,16728,33152,66048,
%T A160620 131584,263160,524936,1050176,2098240,4196952,8389576,16782976,
%U A160620 33555744,67117920,134220712,268453360,536872480,1073780352,2147485448,4295034880,8589944384
%N A160620 a(n) = Sum_{d|n} phi(n/d)^2*2^d.
%H A160620 G. C. Greubel, <a href="/A160620/b160620.txt">Table of n, a(n) for n = 0..1000</a>
%F A160620 Dirichlet (convolution) product of A127473 and A000079. - _R. J. Mathar_, Jun 24 2021
%p A160620 A160620 := proc(n)
%p A160620     if n =0 then
%p A160620         0;
%p A160620     else
%p A160620         add((numtheory[phi](n/d))^2*2^d,d=numtheory[divisors](n)) ;
%p A160620     end if ;
%p A160620 end proc: # _R. J. Mathar_, Jun 24 2021
%t A160620 a[n_]:= If[n<1, 0, Sum[EulerPhi[n/d]^2 * 2^d, {d, Divisors[n]}]]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, May 06 2018 *)
%o A160620 (PARI) a(n) = if (n, sumdiv(n, d, eulerphi(n/d)^2*2^d), 0); \\ _Michel Marcus_, May 07 2018, Jun 22 2021
%Y A160620 Cf. A053635.
%Y A160620 Cf. A000079, A127473.
%K A160620 nonn
%O A160620 0,2
%A A160620 _N. J. A. Sloane_, Nov 21 2009