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a(n) = Sum_{k=1..n} 2^k * phi(k), where phi is the Euler totient function A000010.
1

%I #10 Mar 26 2019 09:04:13

%S 2,6,22,54,182,310,1078,2102,5174,9270,29750,46134,144438,242742,

%T 504886,1029174,3126326,4699190,14136374,22524982,47690806,89633846,

%U 274183222,408400950,1079489590,1884795958,4300715062,7521940534,22554326070,31144260662,95568770102

%N a(n) = Sum_{k=1..n} 2^k * phi(k), where phi is the Euler totient function A000010.

%H Vaclav Kotesovec, <a href="/A324913/a324913.jpg">Plot of a(n)/(n*2^n) for n = 1..100000</a>

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

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

%t Accumulate[Table[2^k*EulerPhi[k], {k, 1, 40}]]

%Y Cf. A000010, A002088, A306988.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Mar 18 2019