OFFSET
1,5
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..53
Eric Weisstein's World of Mathematics, Almost Prime.
Eric Weisstein's World of Mathematics, Semiprime.
FORMULA
a(n) = A082996(2^n).
EXAMPLE
a(6) = 7 because
16 = 2 * 2 * 2 * 2,
24 = 2 * 2 * 2 * 3,
36 = 2 * 2 * 3 * 3,
40 = 2 * 2 * 2 * 5,
54 = 2 * 3 * 3 * 3,
56 = 2 * 2 * 2 * 7, and
60 = 2 * 2 * 3 * 5
are the seven numbers less than 2^6 = 64 that are each the product of four primes.
MATHEMATICA
FourAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@Sqrt[n/(Prime@i*Prime@j)]}]; Array[FourAlmostPrimePi[2^#] &, 37]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Apr 13 2020
STATUS
approved