A099301 Arithmetic derivative of d(n), the number of divisors of n.

0, 1, 1, 1, 1, 4, 1, 4, 1, 4, 1, 5, 1, 4, 4, 1, 1, 5, 1, 5, 4, 4, 1, 12, 1, 4, 4, 5, 1, 12, 1, 5, 4, 4, 4, 6, 1, 4, 4, 12, 1, 12, 1, 5, 5, 4, 1, 7, 1, 5, 4, 5, 1, 12, 4, 12, 4, 4, 1, 16, 1, 4, 5, 1, 4, 12, 1, 5, 4, 12, 1, 16, 1, 4, 5, 5, 4, 12, 1, 7, 1, 4, 1, 16, 4, 4, 4, 12, 1, 16, 4, 5, 4, 4, 4, 16, 1, 5

Offset: 1

Author

T. D. Noe, Oct 12 2004

Keywords

• nonn

References

• See A003415.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A003415 (arithmetic derivative of n).

Programs

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[DivisorSigma[0, n]], {n, 150}]

Formula

a(n) = A003415(A000005(n)).