A306988 - OEIS

%I #20 Feb 06 2024 19:31:24

%S 1,3,8,20,49,117,272,620,1395,3107,6852,14964,32395,69647,149002,

%T 317712,675749,1433769,3033444,6396320,13437913,28130869,58708304,

%U 122239396,254141275,527946013,1096312050,2275897660,4722500707,9791471587,20277706762,41932520528

%N a(n) = Sum_{k=1..n} binomial(n,k)*phi(k), where phi is the Euler totient function.

%H Vaclav Kotesovec, <a href="/A306988/b306988.txt">Table of n, a(n) for n = 1..3280</a>

%H Vaclav Kotesovec, <a href="/A306988/a306988.jpg">Plot of a(n)/(n*2^n) for n = 1..5000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's totient function</a>.

%F a(n) ~ 3 * n * 2^n / Pi^2.

%t Table[Sum[Binomial[n, k]*EulerPhi[k], {k, 1, n}], {n, 1, 40}]

%Y Cf. A000010, A002088, A101509, A160399, A185003.

%Y Partial sums of A131045.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, Mar 18 2019