A229340 Euler totient function of the arithmetic derivative of n: a(n) = phi(n'), a(1) = 0.

0, 1, 1, 2, 1, 4, 1, 4, 2, 6, 1, 8, 1, 6, 4, 16, 1, 12, 1, 8, 4, 12, 1, 20, 4, 8, 18, 16, 1, 30, 1, 32, 6, 18, 4, 16, 1, 12, 8, 32, 1, 40, 1, 16, 24, 20, 1, 48, 6, 24, 8, 24, 1, 54, 8, 44, 10, 30, 1, 44, 1, 20, 32, 64, 6, 60, 1, 24, 12, 58, 1, 48, 1, 24, 40, 32, 6, 70, 1, 80, 36, 42, 1, 60, 10, 24, 16, 48, 1, 80, 8, 32, 16, 42, 8

Offset

1,4

Comments

a(1) = 0 by convention. - Antti Karttunen, Oct 30 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(1) = 0; and for n > 1, a(n) = A000010(A003415(n)).

Example

For n=4 phi(n')=phi(4')=phi(4)=2.
For n=7 phi(n')=phi(7')=phi(1)=1.

Mathematica

Array[EulerPhi@ If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]] &, 75] (* Michael De Vlieger, Oct 30 2017, after Michael Somos at A003415 *)

Prog

(PARI) rd(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]; )); }
a(n) = eulerphi(rd(n)); \\ Michel Marcus, Sep 24 2013

Crossrefs

Cf. A000010, A003415.

Sequence in context: A263432 A286518 A029205 * A322968 A072721 A339792

Adjacent sequences: A229337 A229338 A229339 * A229341 A229342 A229343

Keyword

nonn

Author

Luca Brigada Villa, Sep 24 2013

Extensions

Description/formula clarified and more terms added by Antti Karttunen, Oct 30 2017

Status

approved