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%I #14 Jun 06 2020 04:04:30
%S 1,2,4,6,10,14,22,28,38,50,58,70,86,98,120,144,172,188,208,232,256,
%T 280,320,360,392,432,464,516,552,600,636,684,748,792,864,904,952,1006,
%U 1088,1172,1260,1308,1380,1444,1528,1588,1636,1708,1820,1892,2004,2100,2164
%N a(n) = Sum_{k=1..n} phi(prime(k)-1), where phi is the Euler totient function (A000005).
%D József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 30.
%H Amiram Eldar, <a href="/A333315/b333315.txt">Table of n, a(n) for n = 1..10000</a>
%H S. S. Pillai, <a href="https://doi.org/10.1007/BF03049017">On the sum function connected with primitive roots</a>, Proceedings of the Indian Academy of Sciences - Section A, Vol. 13 (1941), pp. 526-529, <a href="https://www.ias.ac.in/article/fulltext/seca/013/06/0526-0529">alternative link</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Logarithmic_integral_function">Logarithmic integral function</a>.
%F a(n) = Sum_{k=1..n} A008330(k).
%F a(n) ~ A * Li(n^2), where A is Artin's constant (A005596), and Li(x) is the logarithmic integral function.
%t Accumulate @ EulerPhi[Select[Range[300], PrimeQ] - 1]
%o (PARI) a(n) = sum(k=1, n, eulerphi(prime(k)-1)); \\ _Michel Marcus_, Mar 15 2020
%Y Partial sums of A008330.
%Y Cf. A000005, A005596.
%K nonn
%O 1,2
%A _Amiram Eldar_, Mar 14 2020
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