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A141466
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Nonprime transformed products of prime factors of the composites, the largest and smallest prime decremented by 1.
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1, 4, 4, 4, 6, 8, 4, 6, 8, 12, 10, 8, 16, 12, 12, 12, 12, 8, 20, 16, 24, 12, 18, 24, 16, 18, 20, 24, 22, 16, 36, 20, 32, 24, 18, 40, 24, 36, 28, 24, 30, 36, 16, 48, 30, 32, 44, 30, 24, 36, 40, 36, 60, 36, 32, 36, 40, 36, 64, 42, 56, 40, 36, 72, 44, 60, 46, 72, 32, 42, 60, 40, 48, 48, 60, 52
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| In the prime number decomposition of k=A002808(i), i=1,2,3,.., one instance of the largest prime, pmax=A052369(i), is replaced by pmax-1 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin-1. If the product of this modified set of factors, k*(pmax-1)*(pmin-1)/(pmin*pmax), is nonprime, it is added to the sequence.
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EXAMPLE
| If k(1)=4=(p(max)=2)*(p(min)=2), then (2-1)*(2-1)=1*1=1=a(1).
If k(2)=6=(p(max)=3)*(p(min)=2), then (3-1)*(2-1)=2*1=2 (prime).
If k(3)=8=(p(max)=2)*(p=2)*(p(min)=2), then (2-1)*2*(2-1)=1*2*1=2 (prime).
If k(4)=9=(p(max)=3)*(p(min)=3), then (3-1)*(3-1)=2*2=4=a(2).
If k(5)=10=(p(max)=5)*(p(min)=2), then (5-1)*(2-1)=4*1=4=a(3).
If k(6)=12=(p(max)=3)*(p=2)*(p(min)=2), then (3-1)*2*(2-1)=2*2*1=4=a(4).
If k(7)=14=(p(max)=7)*(p(min)=2), then (7-1)*(2-1)=6*1=6=a(5).
If k(8)=15=(p(max)=5)*(p(min)=3), then (5-1)*(3-1)=4*2=8=a(6),
If k(9)=16=(p(max)=2)*2*2*(p(min)=2), then (2-1)*2*2*(2-1)=1*2*2*1=4=a(7).
If k(10)=18=(p(max)=3)*(p=3)*(p(min)=2), then (3-1)*3*(2-1)=2*3*1=6=a(8), etc.
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CROSSREFS
| Sequence in context: A073229 A102126 A097918 * A171743 A171815 A023958
Adjacent sequences: A141463 A141464 A141465 * A141467 A141468 A141469
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KEYWORD
| nonn
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru) Aug 08 2008
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EXTENSIONS
| Definition rephrased by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 14 2008
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