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 A099848 All natural numbers occur in their order as many times as they have ordered prime factorizations. 2
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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) = #{3*2*2, 2*3*2, 2*2*3} = 3, therefore 12 occurs three times. CROSSREFS Cf. A008480. Sequence in context: A071520 A195918 A176842 * A082287 A210062 A006164 Adjacent sequences:  A099845 A099846 A099847 * A099849 A099850 A099851 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 27 2004 STATUS approved

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