A019312 Taxman sequence: define T(S) by max{x+T(S \ {c : c|x})}, where the max is over all x in S for which S also contains a proper divisor of x; if no such x exists, T(S)=0; set T(n)=T({1,...,n}).
0, 2, 3, 7, 9, 15, 17, 21, 30, 40, 44, 50, 52, 66, 81, 89, 93, 111, 113, 124, 144, 166, 170, 182, 198, 224, 251, 279, 285, 301, 303, 319, 352, 386, 418, 442, 448, 486, 503, 525, 529, 571, 573, 617, 660, 706, 710, 734, 758, 808, 833, 885, 891, 940
Offset: 1
Links
- Brian Chess, Table of n, a(n) for n = 1..1000 (Terms 1..158 by Dan Hoey; 159..227 by Timothy Loh; 228..404 by Bernhard Esslinger; 405..519 by van Nek)
- Brian Chess, taxman
- Bernhard Esslinger, CrypTool
- Atli Fannar Franklín and Robert K. Moniot, Polynomial-Time Upper Bound to the Taxman Score
- Dan Hoey, Notes on A019312
- Robert K. Moniot, The Taxman Game
- Brandee Wilson, The Taxman Game
Crossrefs
Cf. A355079.
Programs
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Haskell
import Data.List ((\\), intersect) a019312 = t . enumFromTo 1 where t xs = foldl max 0 [z + t (xs \\ ds) | z <- xs, let ds = a027750_row z, not $ null $ intersect xs $ init ds] -- Reinhard Zumkeller, Apr 05 2015
Formula
When you take a number from S, you must give all its proper divisors to the tax man and there must be at least one to give; T(S) is the maximum total income.
Extensions
Extended by Timothy Loh, Aug 12 2012
Comments