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.

3, 34, 15530, 151165607042

Offset: 1

Author

T. D. Noe, Aug 11 2010

Keywords

• bref
• hard
• more
• nonn

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

Cf. A078840, A125149, A281889.

Extensions

Name edited by Peter Munn, Jan 04 2023