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 A099301 Arithmetic derivative of d(n), the number of divisors of n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 30 23:12 EDT 2021. Contains 346365 sequences. (Running on oeis4.)