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Search: id:A099302
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| A099302 |
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Number of integer solutions to x' = n, where x' is the arithmetic derivative of x. |
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+0
4
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| 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 1, 3, 0, 2, 1, 2, 2, 3, 0, 4, 1, 3, 1, 2, 0, 3, 2, 4, 1, 4, 0, 4, 0, 2, 2, 3, 1, 4, 1, 4, 2, 4, 0, 6, 1, 4, 1, 3, 0, 5, 2, 4, 0, 4, 1, 7, 2, 3, 1, 5, 0, 6, 0, 3, 1, 5, 2, 7, 1, 5, 3, 5, 1, 7, 0, 6, 2, 5, 0, 8, 1, 5, 2, 4, 0, 9, 3, 6, 0, 5, 1, 8, 0, 3, 1, 6, 2, 8, 2, 5, 1, 6
(list; graph; listen)
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OFFSET
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2,9
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COMMENT
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This is the i(n) function in the paper by Ufnarovski and Ahlander. Note that a(1) is infinite because all primes satisfy x' = 1. In general a(n) is greater for even n.
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REFERENCES
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See A003415
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..5000
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MATHEMATICA
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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[Count[d1, n], {n, 2, 400}]
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CROSSREFS
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Cf. A003415 (arithmetic derivative of n), A099303 (greatest x such that x' = n), A098699 (least x such that x' = n), A098700 (n such that x' = n has no integer solution).
Sequence in context: A051585 A049115 A029367 this_sequence A025814 A029354 A035434
Adjacent sequences: A099299 A099300 A099301 this_sequence A099303 A099304 A099305
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Oct 12 2004
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