A116453 Third smallest number with exactly n prime factors.

5, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 147456, 294912, 589824, 1179648, 2359296, 4718592, 9437184, 18874368, 37748736, 75497472, 150994944, 301989888, 603979776, 1207959552, 2415919104, 4831838208, 9663676416, 19327352832, 38654705664

Offset

1,1

Comments

Smallest term in A116451 having exactly n prime factors.

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2).

Formula

a(n) = A116451(A116454(n)) = A116454(n) + 2*n + 3.

a(n) = A005010(n-2) = 9*2^(n - 2) for n > 1.

From Elmo R. Oliveira, Mar 18 2026: (Start)

G.f.: x*(5 - x)/(1 - 2*x).

E.g.f.: (9*exp(2*x) - 9 + 2*x)/4.

a(n) = 2*a(n-1) for n > 2. (End)

Example

a(1) =  5 = A000040(3) > A000040(2) =  3 > A000040(1) =  2.
a(2) =  9 = A001358(3) > A001358(2) =  6 > A001358(1) =  4.
a(3) = 18 = A014612(3) > A014612(2) = 12 > A014612(1) =  8.
a(4) = 36 = A014613(3) > A014613(2) = 24 > A014613(1) = 16.

Mathematica

Join[{5}, 9*2^Range[0, 35]] (* Paolo Xausa, Mar 10 2026 *)

Prog

(Python)
def A116453(n): return 9<<n-2 if n>1 else 5 # Chai Wah Wu, Aug 23 2024

Crossrefs

Cf. A000040, A001358, A005010, A014612, A014613, A116451, A116454.

Sequence in context: A110349 A036832 A257595 * A046578 A046590 A372997

Adjacent sequences: A116450 A116451 A116452 * A116454 A116455 A116456

Keyword

nonn,easy

Author

Reinhard Zumkeller, Feb 16 2006

Extensions

More terms from Paolo Xausa, Mar 10 2026

Status

approved