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

1,2

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.

Formula

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

Mathematica

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

Crossrefs

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

Partial sums of A131045.

Sequence in context: A018792 A360263 A018791 * A026723 A038746 A126876

Adjacent sequences: A306985 A306986 A306987 * A306989 A306990 A306991

Keyword

nonn

Author

Vaclav Kotesovec, Mar 18 2019

Status

approved