id:A019312 - OEIS Search Results

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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}).

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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; listen)

	OFFSET	`1,2`
	COMMENT	`In Germany this is called the Number Shark sequence: see the CrypTool link.`
	LINKS	`Dan Hoey, Table of n, a(n) for n = 1..158` `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: A092293 A096072 A014837 this_sequence A135369 A109660 A075855` `Adjacent sequences: A019309 A019310 A019311 this_sequence 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.`

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Last modified November 23 17:09 EST 2009. Contains 167438 sequences.

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