A306988 a(n) = Sum_{k=1..n} binomial(n,k)*phi(k), where phi is the Euler totient function.

1, 3, 8, 20, 49, 117, 272, 620, 1395, 3107, 6852, 14964, 32395, 69647, 149002, 317712, 675749, 1433769, 3033444, 6396320, 13437913, 28130869, 58708304, 122239396, 254141275, 527946013, 1096312050, 2275897660, 4722500707, 9791471587, 20277706762, 41932520528

Offset: 1

Author

Vaclav Kotesovec, Mar 18 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..3280
• Vaclav Kotesovec, Plot of a(n)/(n*2^n) for n = 1..5000
• Eric Weisstein's World of Mathematics, Totient Function.
• Wikipedia, Euler's totient function.

Crossrefs

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

Partial sums of A131045.

Programs

Mathematica

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

Formula

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