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A099308 Numbers n whose k-th arithmetic derivative is zero for some k. Complement of A099309. 5
0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 25, 29, 30, 31, 33, 34, 37, 38, 41, 42, 43, 46, 47, 49, 53, 57, 58, 59, 61, 62, 65, 66, 67, 70, 71, 73, 77, 78, 79, 82, 83, 85, 89, 93, 94, 97, 98, 101, 103, 105, 107, 109, 113, 114, 118, 121, 126, 127, 129, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The first derivative of 0 and 1 is 0. The second derivative of a prime number is 0.

REFERENCES

See A003415

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

EXAMPLE

18 is on this list because the first through fifth derivatives are 21, 10, 7, 1, 0

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}]; nLim=200; lst={1}; i=1; While[i<=Length[lst], currN=lst[[i]]; pre=Intersection[Flatten[Position[d1, currN]], Range[nLim]]; pre=Complement[pre, lst]; lst=Join[lst, pre]; i++ ]; Union[lst]

CROSSREFS

Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero), A099309 (numbers whose k-th arithmetic derivative is nonzero for all k).

Sequence in context: A188070 A248565 A065896 * A074235 A192189 A285375

Adjacent sequences:  A099305 A099306 A099307 * A099309 A099310 A099311

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 12 2004

STATUS

approved

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Last modified November 19 16:10 EST 2017. Contains 294936 sequences.