login
A099310
Arithmetic derivative of Euler's totient function phi(n).
2
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
LINKS
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 12 2004
STATUS
approved