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

1,6

References

See A003415.

Links

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

Formula

a(n) = A003415(A000005(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[DivisorSigma[0, n]], {n, 150}]

Crossrefs

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

Sequence in context: A080905 A010685 A174571 * A244971 A050347 A240226

Adjacent sequences: A099298 A099299 A099300 * A099302 A099303 A099304

Keyword

nonn

Author

T. D. Noe, Oct 12 2004

Status

approved