A141284 a(n) = (p_max - 1)*...*p*...*(p_min + 2), where p_max*...*p*...*p_min = k(n) = n-th composite.

4, 8, 8, 10, 16, 16, 24, 20, 16, 24, 32, 30, 40, 32, 28, 48, 30, 48, 48, 32, 50, 64, 42, 48, 72, 60, 64, 72, 80, 60, 88, 64, 54, 80, 80, 96, 72, 70, 96, 90, 112, 96, 120, 90, 64, 84, 120, 128, 110, 120, 96, 144, 100, 144, 90, 144, 128, 90, 160, 144, 112, 168, 140, 160

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 08 2008

Keywords

• nonn

Comments

In the prime factorization of the n-th composite, replace one instance of the largest prime factor A052369(n) with A052369(n)-1 and replace one instance of the smallest prime factor A056608(n) with A056608(n)+2.

Examples

			For n=1, k(1) = 4 = (p_max=2)*(p_min=2), so a(1) = (2-1)*(2+2) = 1*4 = 4;
for n=2, k(2) = 6 = (p_max=3)*(p_min=2), so a(2) = (3-1)*(2+2) = 2*4 = 8;
for n=3, k(3) = 8 = (p_max=2)*(p=2)*(p_min=2), so a(3) = (2-1)*2*(2+2) = 1*2*4 = 8; etc.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808.

Programs

Mathematica

Map[Times @@ Flatten[{#[[1]] + 2, #[[2 ;; -2]], #[[-1]] - 1}] &@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &, Select[Range[120], CompositeQ]] (* Michael De Vlieger, Jan 25 2023 *)

Formula

a(n) = A002808(n)*(A052369(n)-1)*(A056608(n)+2)/(A052369(n)*A056608(n)).

Extensions

Definition and examples corrected and entries checked by R. J. Mathar, Mar 29 2010

Simplified by Jon E. Schoenfield, Jan 25 2023