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A110663 Triangle read by rows: T(n,k) = Sum_{j=k..n} phi(j) (1<=k<=n), where phi is Euler's totient function.

%I A110663 #17 Sep 03 2017 17:13:58
%S A110663 1,2,1,4,3,2,6,5,4,2,10,9,8,6,4,12,11,10,8,6,2,18,17,16,14,12,8,6,22,
%T A110663 21,20,18,16,12,10,4,28,27,26,24,22,18,16,10,6,32,31,30,28,26,22,20,
%U A110663 14,10,4,42,41,40,38,36,32,30,24,20,14,10,46,45,44,42,40,36,34,28,24,18,14,4
%N A110663 Triangle read by rows: T(n,k) = Sum_{j=k..n} phi(j) (1<=k<=n), where phi is Euler's totient function.
%H A110663 Indranil Ghosh, <a href="/A110663/b110663.txt">Rows 1..100, flattened</a>
%F A110663 T(n,n) = phi(n) = A000010(n) = number of numbers <=n and relatively prime to n.
%F A110663 T(n,1) = Sum_{j=1..n} phi(j) = A002088(n).
%e A110663 T(5,3) = 8 because phi(3)+phi(4)+phi(5) = 2+2+4 = 8.
%e A110663 Triangle begins:
%e A110663 1;
%e A110663 2,1;
%e A110663 4,3,2;
%e A110663 6,5,4,2;
%e A110663 10,9,8,6,4;
%e A110663 ...
%t A110663 T[n_, n_] := EulerPhi[n]; T[n_, k_] := Sum[EulerPhi[j], {j, k, n}];
%t A110663 Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Sep 03 2017 *)
%o A110663 (PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(sum(j=k, n, eulerphi(j)), ", ");); print(););} \\ _Michel Marcus_, Apr 05 2015
%Y A110663 Cf. A000010, A002088.
%K A110663 nonn,tabl
%O A110663 1,2
%A A110663 _Emeric Deutsch_, Aug 02 2005