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 A287484 Number of squarefree k with A002110(n) <= k < A002110(n+1) such that A001221(k) = n. 3
 1, 3, 7, 19, 58, 152, 422, 995, 2359, 6294, 14507, 36370, 88198, 187786, 386993, 840033, 1901930, 3851372, 8088478, 16388857, 30001902, 56613547, 103229263, 193020113, 389750880, 759988983, 1359250012, 2350842201, 3737393021, 5748044055, 10843131073, 19774152370 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A001221, A002110, A005117, A006881, A033992. Sequence in context: A263334 A005506 A268125 * A201169 A148667 A148668 Adjacent sequences:  A287481 A287482 A287483 * A287485 A287486 A287487 KEYWORD nonn,hard AUTHOR Michael De Vlieger, May 25 2017 EXTENSIONS a(25)-a(31) from David A. Corneth, May 31 2017 STATUS approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)