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Search: id:A098700
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| A098700 |
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Numbers n such that x' = n has no integer solution, where x' is the arithmetic derivative of x. |
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+0
5
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| 2, 3, 11, 17, 23, 29, 35, 37, 47, 53, 57, 65, 67, 79, 83, 89, 93, 97, 107, 117, 125, 127, 137, 145, 149, 157, 163, 173, 177, 179, 189, 197, 205, 207, 209, 217, 219, 223, 233, 237, 245, 257, 261, 277, 289, 303, 305, 307, 317, 323, 325, 337, 345, 353, 367, 373
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If x' = n has solutions, they occur for x <= (n/2)^2. - T. D. Noe (noe(AT)sspectra.com), Oct 12 2004
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..752
Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003. (See p. 7.)
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MATHEMATICA
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a[1] = 0; a[n_] := Block[{f = Transpose[ FactorInteger[ n]]}, If[ PrimeQ[n], 1, Plus @@ (n*f[[2]]/f[[1]])]]; b = Table[ -1, {500}]; b[[1]] = 1; Do[c = a[n]; If[c < 500 && b[[c + 1]] == 0, b[[c + 1]] = n], {n, 10^6}]; Select[ Range[500], b[[ # ]] == 0 &]
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}]; Select[Range[400], 0==Count[d1, # ]&]
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CROSSREFS
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Cf. A003415 (arithmetic derivative of n), A099302 (number of solutions to x' = n), A099303 (greatest x such that x' = n), A098699 (least x such that x' = n).
Adjacent sequences: A098697 A098698 A098699 this_sequence A098701 A098702 A098703
Sequence in context: A014092 A100962 A045337 this_sequence A025584 A105903 A045338
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 21 2004
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Oct 12 2004
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