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A099848
All natural numbers occur in their order as many times as they have ordered prime factorizations.
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
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.
PROG
(Haskell)
a099848 n = a099848_list !! (n-1)
a099848_list = concat $ zipWith replicate a008480_list [1..]
-- Reinhard Zumkeller, Nov 19 2015
CROSSREFS
Cf. A008480.
Sequence in context: A291764 A319681 A340767 * A082287 A331267 A238839
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 27 2004
STATUS
approved