A324913 a(n) = Sum_{k=1..n} 2^k * phi(k), where phi is the Euler totient function A000010.

2, 6, 22, 54, 182, 310, 1078, 2102, 5174, 9270, 29750, 46134, 144438, 242742, 504886, 1029174, 3126326, 4699190, 14136374, 22524982, 47690806, 89633846, 274183222, 408400950, 1079489590, 1884795958, 4300715062, 7521940534, 22554326070, 31144260662, 95568770102

Offset: 1

Author

Vaclav Kotesovec, Mar 18 2019

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..3293
• Vaclav Kotesovec, Plot of a(n)/(n*2^n) for n = 1..100000
• Eric Weisstein's World of Mathematics, Totient Function
• Wikipedia, Euler's totient function

Crossrefs

Cf. A000010, A002088, A306988.

Programs

Maple

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

Mathematica

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