|
Search: id:A099304
|
|
|
| A099304 |
|
Least k > 0 such that (n+k)' = n' + k', where n' denotes the arithmetic derivative of n. |
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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
|
|
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}]
|
|
CROSSREFS
|
Cf. A003415 (arithmetic derivative of n), A099305 (number of solutions to (n+k)' = n' + k').
Sequence in context: A050457 A076891 A071883 this_sequence A064680 A057560 A085592
Adjacent sequences: A099301 A099302 A099303 this_sequence A099305 A099306 A099307
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Oct 12 2004
|
|
|
Search completed in 0.002 seconds
|
