A099310 Arithmetic derivative of Euler's totient function phi(n).

0, 0, 1, 1, 4, 1, 5, 4, 5, 4, 7, 4, 16, 5, 12, 12, 32, 5, 21, 12, 16, 7, 13, 12, 24, 16, 21, 16, 32, 12, 31, 32, 24, 32, 44, 16, 60, 21, 44, 32, 68, 16, 41, 24, 44, 13, 25, 32, 41, 24, 80, 44, 56, 21, 68, 44, 60, 32, 31, 32, 92, 31, 60, 80, 112, 24, 61, 80, 48, 44, 59, 44, 156, 60

Offset

1,5

References

See A003415

Links

Michel Marcus, Table of n, a(n) for n = 1..5000

Formula

a(n) = A003415(A000010(n))

Mathematica

dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; Table[dn[EulerPhi[n]], {n, 100}]

Prog

(GAP)
A099310:= Concatenation([0, 0], List(List(List([3..10^3], n->Phi(n)), Factors), i->Product(i)*Sum(i, j->1/j))); # Muniru A Asiru, Sep 27 2017
(PARI) ad(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]);
a(n) = ad(eulerphi(n)); \\ Michel Marcus, Sep 29 2017

Crossrefs

Cf. A003415 (arithmetic derivative of n).

Sequence in context: A104571 A249057 A105721 * A021880 A075013 A117379

Adjacent sequences: A099307 A099308 A099309 * A099311 A099312 A099313

Keyword

nonn

Author

T. D. Noe, Oct 12 2004

Status

approved