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A058933
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Let k be bigomega(n) (i.e., n is a k-almost-prime). a(n) = number of k-almost-primes <= n.
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12
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1, 1, 2, 1, 3, 2, 4, 1, 3, 4, 5, 2, 6, 5, 6, 1, 7, 3, 8, 4, 7, 8, 9, 2, 9, 10, 5, 6, 10, 7, 11, 1, 11, 12, 13, 3, 12, 14, 15, 4, 13, 8, 14, 9, 10, 16, 15, 2, 17, 11, 18, 12, 16, 5, 19, 6, 20, 21, 17, 7, 18, 22, 13, 1, 23, 14, 19, 15, 24, 16, 20, 3, 21, 25, 17, 18, 26, 19, 22, 4, 8, 27, 23
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OFFSET
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1,3
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COMMENTS
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Equivalently, the number of positive integers less than or equal to n with the same number of prime factors as n, counted with multiplicity. - Gus Wiseman, Dec 28 2018
There is a close relationship between a(n) and a(n^2). See A209934 for an exploratory quantification. - Peter Munn, Aug 04 2019
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LINKS
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FORMULA
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EXAMPLE
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3 is prime, so a(3)=2. 10 is 2-almost prime (semiprime), so a(10)=4.
Column n lists the a(n) positive integers less than or equal to n with the same number of prime factors as n, counted with multiplicity:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
---------------------------------------------------------------------
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 3 4 5 6 9 7 8 11 10 14 13 12 17 18
2 3 4 6 5 7 9 10 11 8 13 12
2 4 3 5 6 9 7 11 8
2 3 4 6 5 7
2 4 3 5
2 3
2
(End)
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MAPLE
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p:= proc() 0 end:
a:= proc(n) option remember; local t;
t:= numtheory[bigomega](n);
p(t):= p(t)+1
end:
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MATHEMATICA
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PROG
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(PARI) a(n) = my(k=bigomega(n)); sum(i=1, n, bigomega(i)==k); \\ Michel Marcus, Jun 27 2024
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CROSSREFS
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Cf. A000010, A000961, A001222, A006049, A045920, A061142, A067003, A078843, A209934, A302242, A322838, A322839, A322840.
Equivalent sequence restricted to squarefree numbers: A340313.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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