A289173 The largest n-almost prime less than 3^n.

2, 6, 20, 60, 208, 624, 2080, 6240, 18720, 58240, 176000, 529408, 1593344, 4780032, 14344192, 43040768, 129138688, 387416064, 1162248192, 3486777344, 10460332032, 31380996096, 94142988288, 282428964864, 847286894592, 2541860683776, 7625582051328

Offset

1,1

Comments

All terms are even as 3^n is the first odd n-almost prime.

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..100

Example

a(26) = 2541860683776 = 3^26 - 5144553 = 2^18*3^6*47*283 (a 26-almost prime).
From Michael De Vlieger, Jun 27 2017: (Start)
Table of prime factors of a(n) for 1 <= n <= 16:
   1:  2
   2:  2   3
   3:  2   2   5
   4:  2   2   3   5
   5:  2   2   2   2  13
   6:  2   2   2   2   3  13
   7:  2   2   2   2   2   5  13
   8:  2   2   2   2   2   3   5  13
   9:  2   2   2   2   2   3   3   5  13
  10:  2   2   2   2   2   2   2   5   7  13
  11:  2   2   2   2   2   2   2   5   5   5  11
  12:  2   2   2   2   2   2   2   2   2   2  11  47
  13:  2   2   2   2   2   2   2   2   2   2   2   2 389
  14:  2   2   2   2   2   2   2   2   2   2   2   2   3 389
  15:  2   2   2   2   2   2   2   2   2   2   2   2   2  17 103
  16:  2   2   2   2   2   2   2   2   2   2   2   2   2   2  37  71(End)

Mathematica

Table[SelectFirst[Range[3^n - 1, 2^n, -1], PrimeOmega@ # == n &], {n, 18}] (* Michael De Vlieger, Jun 27 2017 *)

Prog

(PARI) for (n = 1, 26, m = 3^n-1; while(bigomega(m) <> n, m = m-2); print1 (m ", "))
(PARI) a(n)=my(target=n-1); forstep(k=3^n\2, 1, -1, if(bigomega(k)==target, return(2*k))) \\ Charles R Greathouse IV, Jul 05 2017

Crossrefs

Cf. A078843 (where 3^n occurs in n-almost primes).

Sequence in context: A134293 A363107 A136883 * A057766 A132353 A263900

Adjacent sequences: A289170 A289171 A289172 * A289174 A289175 A289176

Keyword

nonn

Author

Zak Seidov, Jun 26 2017

Extensions

a(27) from Jon E. Schoenfield, Jul 02 2017

Status

approved