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%I #16 Sep 11 2024 00:35:46
%S 1,2,8,12,40,24,108,88,168,128,420,184,696,384,576,640,1536,612,2160,
%T 1024,1680,1500,3784,1440,4000,2544,4140,2904,7560,2224,9240,5184,
%U 6880,5760,9216,4752,15552,8100,11376,7840,21200,6504,24528,12080,15072,14300
%N a(n) = A000010(n) * A002088(n).
%H Nathaniel Johnston, <a href="/A143231/b143231.txt">Table of n, a(n) for n = 1..2500</a>
%F a(n) = A000010(n) * A002088(n).
%F a(n) = Sum_{k=1..n} A143230(n,k) (row sums of A143230).
%e a(5) = 40 = A000010(5) * A002088(5) = 4 * 10.
%e a(5) = 40 = sum of row 5 terms of triangle A143230: (4 + 4 + 8 + 8 + 16).
%p with(numtheory):
%p a := proc(n) return phi(n)*add(phi(k),k=1..n): end:
%p seq(a(n),n=1..46); # _Nathaniel Johnston_, Jun 26 2011
%t a[n_]:= a[n]= EulerPhi[n]*Sum[EulerPhi[k], {k,n}];
%t Table[a[n], {n,50}] (* _G. C. Greubel_, Sep 10 2024 *)
%o (PARI) a(n)=sum(k=1, n, eulerphi(k))*eulerphi(n) \\ _Charles R Greathouse IV_, Feb 21 2013
%o (Magma)
%o A143231:= func< n | EulerPhi(n)*(&+[EulerPhi(k): k in [1..n]]) >;
%o [A143231(n): n in [1..50]]; // _G. C. Greubel_, Sep 10 2024
%o (SageMath)
%o def A143231(n): return euler_phi(n)*sum(euler_phi(k) for k in range(1,n+1))
%o [A143231(n) for n in range(1,51)] # _G. C. Greubel_, Sep 10 2024
%Y Cf. A000010, A002088, A143230.
%K nonn,changed
%O 1,2
%A _Gary W. Adamson_, Jul 31 2008
%E Terms after a(14) from _Nathaniel Johnston_, Jun 26 2011
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