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%I #19 Aug 18 2021 11:56:56
%S 1,3,7,15,23,35,59,83,107,147,187,235,307,355,419,547,643,751,895,991,
%T 1111,1331,1507,1667,1907,2123,2339,2675,2899,3139,3619,3939,4259,
%U 4643,4931,5363,6011,6443,6827,7467,7947,8451,9291,9771,10299,11311,12047,12719,13559,14199,14967,16215,17151,17871,18831
%N a(n) = Sum_{i=1..n} phi(i)*phi(i+1), where phi(n) = A000010(n) is Euler's totient function.
%D József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 32.
%H Amiram Eldar, <a href="/A330319/b330319.txt">Table of n, a(n) for n = 1..10000</a>
%H A. E. Ingham, <a href="https://doi.org/10.1112/jlms/s1-2.3.202">Some asymptotic formulae in the theory of numbers</a>, Journal of the London Mathematical Society, Vol. s1-2, No. 3 (1927), pp. 202-208.
%H L. Mirsky, <a href="http://doi.org/10.1215/S0012-7094-49-01625-7">Summation formula involving arithmetic functions</a>, Duke Mathematical Journal, Vol. 16, No. 2 (1949), pp. 261-272.
%F a(n) ~ (c/3) * n^3 + O(n^2*log(n)^2), where c = Product_{p prime}(1 - 2/p^2) (A065474). - _Amiram Eldar_, Mar 05 2020
%t phi = EulerPhi[Range[56]]; Accumulate[Most[phi] * Rest[phi]] (* _Amiram Eldar_, Mar 05 2020 *)
%o (PARI) a(n) = sum(i=1, n, eulerphi(i)*eulerphi(i+1)); \\ _Michel Marcus_, Mar 05 2020
%Y Cf. A000010, A065474, A335131.
%Y Partial sums of A083542.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Dec 11 2019
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