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A180126
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a(n) is the least k such that for numbers x >= k, PrimePi(n,x) > PrimePi(n-1,x), where PrimePi(n,x) is the number of n-almost-primes <= x.
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1
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OFFSET
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1,1
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COMMENTS
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Note that a(n) is an n-almost-prime. An n-almost-prime is a number having exactly n prime factors (counted with multiplicity). So 1 is the only 0-almost-prime; 1-almost-primes are the usual prime numbers; 2-almost-primes are also called semiprimes. The first three terms are mentioned in A125149.
For 2 <= n <= 4, the values for a(n)/a(n-1) (11.3, 456.8, 9733780.2) are each a little larger than A281889(n), "the median n-th least prime factor of the integers". - Peter Munn, Jan 04 2023
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LINKS
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CROSSREFS
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KEYWORD
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bref,hard,more,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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