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

Offset: 1

Author

Reinhard Zumkeller, Feb 16 2006

Keywords

• nonn
• easy

Comments

Smallest term in A116451 having exactly n prime factors;

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

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

Examples

			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.
		

Links

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

Programs

Python

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