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

0, 1, 2, 4, 7, 12, 18, 27, 38, 52, 68, 89, 112, 141, 173, 209, 249, 297, 348, 408, 472, 542, 617, 703, 793, 893, 999, 1114, 1235, 1370, 1509, 1663, 1825, 1997, 2177, 2369, 2567, 2783, 3008, 3245, 3490, 3755, 4026, 4318

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A005598, A046657, A049695.

Programs

Magma

A049703:= func< n | n eq 0 select 0 else (1 +(&+[(n-j+1)*EulerPhi(j): j in [1..n]]))/2 >;
[A049703(n): n in [0..60]]; // G. C. Greubel, Dec 08 2022

Mathematica

A005598[n_]:= A005598[n]= 1 +Sum[(n-j+1)*EulerPhi[j], {j,n}];
A049703[n_]:= If[n==0, 0, A005598[n]/2];
Table[A049703[n], {n,0,50}] (* G. C. Greubel, Dec 08 2022 *)

SageMath

@CachedFunction
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
[A049703(n) for n in range(61)] # G. C. Greubel, Dec 08 2022

Formula

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

a(n) = (1/2)*(1 + (n+1)*A002088(n) - A011755(n)), with a(0) = 0. - G. C. Greubel, Dec 08 2022

Extensions

Edited by N. J. A. Sloane, Apr 04 2007.