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A334069
Number of numbers <= 2^n that are the product of exactly four primes, not necessarily distinct.
3
0, 0, 0, 1, 2, 7, 14, 34, 71, 152, 325, 669, 1405, 2866, 5931, 12139, 24782, 50444, 102458, 207945, 420511, 850518, 1716168, 3460304, 6968639, 14022029, 28189833, 56631732, 113697179, 228115641, 457456902, 916899721, 1836996851, 3678943569, 7365141297, 14740076678, 29490954290
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
Partial sums of A120035.
Sequence in context: A286861 A290682 A000147 * A128902 A227213 A319455
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Apr 13 2020
STATUS
approved