cp's OEIS Frontend

A049703 a(0) = 0; for n>0, a(n) = A005598(n)/2.

%I A049703 #14 Dec 09 2022 07:15:50
%S A049703 0,1,2,4,7,12,18,27,38,52,68,89,112,141,173,209,249,297,348,408,472,
%T A049703 542,617,703,793,893,999,1114,1235,1370,1509,1663,1825,1997,2177,2369,
%U A049703 2567,2783,3008,3245,3490,3755,4026,4318
%N A049703 a(0) = 0; for n>0, a(n) = A005598(n)/2.
%H A049703 G. C. Greubel, <a href="/A049703/b049703.txt">Table of n, a(n) for n = 0..5000</a>
%F A049703 a(n) = (1/2)*Sum_{j=0..n} T(j, n-j), for array T in A049695.
%F A049703 a(n) = (1/2)*(1 + (n+1)*A002088(n) - A011755(n)), with a(0) = 0. - _G. C. Greubel_, Dec 08 2022
%t A049703 A005598[n_]:= A005598[n]= 1 +Sum[(n-j+1)*EulerPhi[j], {j,n}];
%t A049703 A049703[n_]:= If[n==0, 0, A005598[n]/2];
%t A049703 Table[A049703[n], {n,0,50}] (* _G. C. Greubel_, Dec 08 2022 *)
%o A049703 (Magma)
%o A049703 A049703:= func< n | n eq 0 select 0 else (1 +(&+[(n-j+1)*EulerPhi(j): j in [1..n]]))/2 >;
%o A049703 [A049703(n): n in [0..60]]; // _G. C. Greubel_, Dec 08 2022
%o A049703 (SageMath)
%o A049703 @CachedFunction
%o A049703 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 [A049703(n) for n in range(61)] # _G. C. Greubel_, Dec 08 2022
%Y A049703 Cf. A005598, A046657, A049695.
%K A049703 nonn
%O A049703 0,3
%A A049703 _Clark Kimberling_
%E A049703 Edited by _N. J. A. Sloane_, Apr 04 2007.