OFFSET
0,2
COMMENTS
Primorial A002110(n) is the smallest squarefree number with n prime factors. a(n) is a list of squarefree numbers with n prime factors greater than and including A002110(n) but less than A002110(n+1).
a(1) counts the first primes less than 6.
a(2) counts the first squarefree semiprimes (A006881) less than 30.
a(3) counts the smallest terms of A033992 less than 210, etc.
LINKS
Eric Weisstein's World of Mathematics, Primorial
Eric Weisstein's World of Mathematics, Squarefree
EXAMPLE
Let p_n# = A002110(n).
a(0) = 1 since the only squarefree number between p_0# and (p_1# - 1) (i.e., 1 and 1) with 0 prime factors is 1.
a(1) = 3 since for p_1# <= k <= (p_2# - 1), i.e., 2 <= k <= 5, there are three primes {2, 3, 5}.
a(2) = 7 since we find the squarefree semiprimes {6, 10, 14, 15, 21, 22, 26} between 6 and 29 inclusive.
MATHEMATICA
Table[Count[Range[#, Prime[n + 1] # - 1] &@ Product[Prime@ i, {i, n}], k_ /; And[SquareFreeQ@ k, PrimeOmega@ k == n]], {n, 0, 6}]
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Michael De Vlieger, May 25 2017
EXTENSIONS
a(25)-a(31) from David A. Corneth, May 31 2017
STATUS
approved