A324913 - OEIS

A324913

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

%I #18 Jun 28 2026 15:48:16

%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 Robert Israel, <a href="/A324913/b324913.txt">Table of n, a(n) for n = 1..3293</a>

%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="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>

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

%p ListTools:-PartialSums([seq(2^k * numtheory:-phi(k),k=1..50)]); # _Robert Israel_, Apr 17 2025

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

%Y Cf. A000010, A002088, A306988.

%K nonn,changed

%O 1,1

%A _Vaclav Kotesovec_, Mar 18 2019