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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}). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In Germany this is called the Number Shark sequence: see the CrypTool link.

LINKS

Dan Hoey and Timothy Loh, Table of n, a(n) for n = 1..227 (Terms 1 through 158 were computed by Dan Hoey; terms 159 through 227 by Timothy Loh)

Bernhard Esslinger, CrypTool

Dan Hoey, Notes on A019312

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.

CROSSREFS

Sequence in context: A215485 A096072 A014837 * A135369 A211539 A109660

Adjacent sequences:  A019309 A019310 A019311 * A019313 A019314 A019315

KEYWORD

nonn,nice

AUTHOR

Dan Hoey (Hoey(AT)AIC.NRL.Navy.Mil)

EXTENSIONS

There was a suggestion that a(54) (= 940) is incorrect, but it is OK.

Extended by Timothy Loh, Aug 12 2012

STATUS

approved

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Last modified April 21 11:59 EDT 2014. Contains 240824 sequences.