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A099304 Least k > 0 such that (n+k)' = n' + k', where n' denotes the arithmetic derivative of n. 4
2, 1, 6, 2, 10, 3, 14, 4, 18, 5, 14, 6, 26, 7, 30, 8, 34, 9, 38, 10, 42, 11, 46, 12, 50, 13, 54, 14, 26, 15, 62, 16, 42, 17, 4, 18, 74, 19, 78, 20, 82, 21, 86, 22, 90, 23, 38, 24, 98, 25, 102, 26, 106, 27, 27, 28, 114, 29, 118, 30, 122, 31, 126, 32, 130, 33, 18, 34, 138, 8, 142 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The arithmetic derivative does not, in general, have the linearity property. In most cases, a(n) = n/2 for even n and a(n) = 2n for odd n.

REFERENCES

See A003415

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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[k=1; While[dn[n]+dn[k] != dn[n+k], k++ ]; k, {n, 100}]

PROG

(Haskell)

import Data.List (find)

import Data.Maybe (fromJust)

a099304 n = succ $ fromJust $ elemIndex 0 $

   zipWith (-) (drop (fromInteger n + 1) a003415_list)

               (map (+ n') $ tail a003415_list)

   where n' = a003415 n

-- Reinhard Zumkeller, May 09 2011

CROSSREFS

Cf. A003415 (arithmetic derivative of n), A099305 (number of solutions to (n+k)' = n' + k').

Sequence in context: A239537 A076891 A071883 * A064680 A239148 A057560

Adjacent sequences:  A099301 A099302 A099303 * A099305 A099306 A099307

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 12 2004

STATUS

approved

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Last modified September 25 20:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)