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A180126
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.
1
3, 34, 15530, 151165607042
OFFSET
1,1
COMMENTS
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
CROSSREFS
KEYWORD
bref,hard,more,nonn
AUTHOR
T. D. Noe, Aug 11 2010
EXTENSIONS
Name edited by Peter Munn, Jan 04 2023
STATUS
approved