

A099303


Greatest integer x such that x' = n, or 0 if there is no such x, where x' is the arithmetic derivative of x.


9



0, 0, 4, 6, 9, 10, 15, 14, 25, 0, 35, 22, 49, 26, 55, 0, 77, 34, 91, 38, 121, 0, 143, 46, 169, 27, 187, 0, 221, 58, 247, 62, 289, 0, 323, 0, 361, 74, 391, 42, 437, 82, 403, 86, 529, 0, 551, 94, 589, 63, 667, 0, 713, 106, 703, 0, 841, 70, 899, 118, 961, 122, 943, 0, 1073, 0
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OFFSET

2,3


COMMENTS

This is the largest member of the set I(n) in the paper by Ufnarovski and Ahlander. They show that a(n) <= (n/2)^2.
Because this sequence is quite different for even and odd n, it is bisected into A102084 and A189762. The upper bound for odd n appears to be (n/3)^(3/2), which is attained when n = 3p^2 for primes p>5.  T. D. Noe, Apr 27 2011


REFERENCES

See A003415


LINKS

T. D. Noe, Table of n, a(n) for n=2..1000


MATHEMATICA

dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; d1=Table[dn[n], {n, 40000}]; Table[x=Max[Flatten[Position[d1, n]]]; If[x>Infinity, x, 0], {n, 2, 400}]


CROSSREFS

Cf. A003415 (arithmetic derivative of n), A099302 (number of solutions to x' = n), A098699 (least x such that x' = n), A098700 (n such that x' = n has no integer solution).
Sequence in context: A200677 A189553 A189482 * A243485 A310665 A005659
Adjacent sequences: A099300 A099301 A099302 * A099304 A099305 A099306


KEYWORD

nonn


AUTHOR

T. D. Noe, Oct 12 2004


STATUS

approved



