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a(0) = 0; for n>0, a(n) = A005598(n)/2.
4

%I #14 Dec 09 2022 07:15:50

%S 0,1,2,4,7,12,18,27,38,52,68,89,112,141,173,209,249,297,348,408,472,

%T 542,617,703,793,893,999,1114,1235,1370,1509,1663,1825,1997,2177,2369,

%U 2567,2783,3008,3245,3490,3755,4026,4318

%N a(0) = 0; for n>0, a(n) = A005598(n)/2.

%H G. C. Greubel, <a href="/A049703/b049703.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = (1/2)*Sum_{j=0..n} T(j, n-j), for array T in A049695.

%F a(n) = (1/2)*(1 + (n+1)*A002088(n) - A011755(n)), with a(0) = 0. - _G. C. Greubel_, Dec 08 2022

%t A005598[n_]:= A005598[n]= 1 +Sum[(n-j+1)*EulerPhi[j], {j,n}];

%t A049703[n_]:= If[n==0, 0, A005598[n]/2];

%t Table[A049703[n], {n,0,50}] (* _G. C. Greubel_, Dec 08 2022 *)

%o (Magma)

%o A049703:= func< n | n eq 0 select 0 else (1 +(&+[(n-j+1)*EulerPhi(j): j in [1..n]]))/2 >;

%o [A049703(n): n in [0..60]]; // _G. C. Greubel_, Dec 08 2022

%o (SageMath)

%o @CachedFunction

%o def A049703(n): return 0 if (n==0) else (1 + sum((n-j+1)*euler_phi(j) for j in range(1,n+1)))/2

%o [A049703(n) for n in range(61)] # _G. C. Greubel_, Dec 08 2022

%Y Cf. A005598, A046657, A049695.

%K nonn

%O 0,3

%A _Clark Kimberling_

%E Edited by _N. J. A. Sloane_, Apr 04 2007.