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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 14 04:56 EST 2019. Contains 329110 sequences. (Running on oeis4.)