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a(n) = (p_max - 1)*...*p*...*(p_min + 2), where p_max*...*p*...*p_min = k(n) = n-th composite.
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%I #11 Jan 25 2023 10:01:34

%S 4,8,8,10,16,16,24,20,16,24,32,30,40,32,28,48,30,48,48,32,50,64,42,48,

%T 72,60,64,72,80,60,88,64,54,80,80,96,72,70,96,90,112,96,120,90,64,84,

%U 120,128,110,120,96,144,100,144,90,144,128,90,160,144,112,168,140,160

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

%C 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.

%H Michael De Vlieger, <a href="/A141284/b141284.txt">Table of n, a(n) for n = 1..10000</a>

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

%e For n=1, k(1) = 4 = (p_max=2)*(p_min=2), so a(1) = (2-1)*(2+2) = 1*4 = 4;

%e for n=2, k(2) = 6 = (p_max=3)*(p_min=2), so a(2) = (3-1)*(2+2) = 2*4 = 8;

%e 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.

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

%Y Cf. A002808.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Aug 08 2008

%E Definition and examples corrected and entries checked by _R. J. Mathar_, Mar 29 2010

%E Simplified by _Jon E. Schoenfield_, Jan 25 2023