id:A099848 - OEIS Search Results

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All natural numbers occur in their order as many times as they have ordered prime factorizations.

+0
3

1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 15, 16, 17, 18, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 23, 24, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30, 30, 30, 30, 30, 31, 32, 33, 33, 34, 34, 35, 35, 36, 36, 36, 36, 36, 36, 37, 38, 38, 39, 39, 40 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`n occurs exactly once iff n is a prime power (A000961);` `n occurs exactly twice iff n is a semiprime with distinct factors (A006881);` `a(A099849(n) - k) = n for 0 <= k < A008480(n).`
	LINKS	`Eric Weisstein's World of Mathematics, Prime Factorization`
	EXAMPLE	`n = 12: A008480(12) = #{322, 232, 223} = 3, therefore 12 occurs three times.`
	CROSSREFS	`Cf. A008480.` `Sequence in context: A025548 A121604 A071520 this_sequence A082287 A006164 A053758` `Adjacent sequences: A099845 A099846 A099847 this_sequence A099849 A099850 A099851`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2004`

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Last modified November 21 14:49 EST 2008. Contains 150807 sequences.

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