A131045 Binomial transform of Euler's totient function phi(n+1).

1, 2, 5, 12, 29, 68, 155, 348, 775, 1712, 3745, 8112, 17431, 37252, 79355, 168710, 358037, 758020, 1599675, 3362876, 7041593, 14692956, 30577435, 63531092, 131901879, 273804738, 568366037, 1179585610, 2446603047, 5068970880

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{j=0..n} binomial(n,j)*phi(j+1). - Emeric Deutsch, Jul 09 2007

Example

a(3) = (1,3,3,1) dot (1,1,2,2) = 1 + 3 + 6 + 2 = 12.

Maple

with(numtheory); a := proc (n) options operator, arrow; sum(binomial(n, j)*phi(j+1), j = 0 .. n) end proc; seq(a(n), n = 0 .. 30); # Emeric Deutsch, Jul 09 2007

Mathematica

Table[Sum[Binomial[n, k]*EulerPhi[k+1], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 30 2017 *)

Prog

(PARI) a(n) = sum(j=0, n, binomial(n, j)*eulerphi(j+1)); \\ Michel Marcus, Feb 26 2019

Crossrefs

Cf. A000010, A007318.

Sequence in context: A320553 A266465 A079864 * A182555 A026721 A094975

Adjacent sequences: A131042 A131043 A131044 * A131046 A131047 A131048

Keyword

nonn

Author

Gary W. Adamson, Jun 11 2007

Extensions

More terms from Emeric Deutsch, Jul 09 2007

Status

approved