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A141284 a(n) = (p_max - 1)*...*p*...*(p_min + 2), where p_max*...*p*...*p_min = k(n) = n-th composite. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
LINKS
FORMULA
a(n) = A002808(n)*(A052369(n)-1)*(A056608(n)+2)/(A052369(n)*A056608(n)).
EXAMPLE
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.
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 *)
CROSSREFS
Cf. A002808.
Sequence in context: A187768 A344984 A335212 * A272812 A273207 A145154
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition and examples corrected and entries checked by R. J. Mathar, Mar 29 2010
Simplified by Jon E. Schoenfield, Jan 25 2023
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)