A064450 Sum of totients of binomial coefficients C(n,j), j=0..n.

1, 2, 3, 6, 8, 18, 30, 86, 106, 158, 290, 662, 1410, 3674, 7166, 16242, 20242, 46754, 72910, 162686, 304866, 524570, 1179430, 2842710, 5230210, 11035402, 24478394, 40473686, 63927602, 155016682, 328928338, 888801182, 928681474, 1765045802

Offset

0,2

Comments

a(n) = sum of n-th row of the triangle formed by replacing each m in Pascal's triangle by phi(m). See A102715.

Links

Harry J. Smith, Table of n, a(n) for n = 0..200

Example

For n=4, the binomial coefficients C(4,j) are 1, 4, 6, 4, and 1. The totients are 1, 2, 2, 2, and 1.  So a(4) = 1 + 2 + 2 + 2 + 1 = 8. - Michael B. Porter, Jun 25 2018

Mathematica

a(n)=Apply[Plus, Table[EulerPhi[Binomial[n, w]], {w, 0, n}]],

Prog

(PARI) { for (n=0, 200, a=sum(j=0, n, eulerphi(binomial(n, j))); write("b064450.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 14 2009
(PARI) a(n) = vecsum(vector(n+1, k, eulerphi(binomial(n, k-1)))); \\ Michel Marcus, Jun 24 2018

Crossrefs

Cf. A000010, A102715.

Sequence in context: A005508 A022542 A220418 * A217137 A248824 A130623

Adjacent sequences: A064447 A064448 A064449 * A064451 A064452 A064453

Keyword

nonn

Author

Labos Elemer, Oct 02 2001

Status

approved