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A141462
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Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2, the smallest by 1.
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0
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0, 1, 0, 6, 0, 6, 10, 9, 4, 12, 6, 10, 9, 0, 18, 15, 20, 6, 22, 12, 15, 18, 18, 21, 8, 30, 15, 30, 22, 9, 36, 20, 34, 27, 18, 30, 0, 44, 27, 30, 42, 25, 12, 35, 30, 34, 54, 33, 24, 18, 39, 30, 60, 54, 36, 27, 66, 42, 58, 45, 68, 16, 35, 54, 30, 45, 44, 50, 51, 18, 45, 70, 40, 51, 84
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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-2 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-2)*(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 a(1)=(2-2)*(2-1)=0*1=0 =a(1).
If k(2)=6=(p(max)=3)*(p(min)=2), then a(2)=(3-2)*(2-1)=1*1=1=a(2).
If k(3)=8=(p(max)=2)*(p=2)*(p(min)=2), then a(3)=(2-2)*2*(2-1)=0*2*1=0=a(3).
If k(4)=9=(p(max)=3)*(p(min)=3), then (3-2)*(3-1)=1*2=2 (prime).
If k(5)=10=(p(max)=5)*(p(min)=2), then (5-2)*(2-1)=3*1=3 (prime).
If k(6)=12=(p(max)=3)*(p=2)*(p(min)=2), then (3-2)*2*(2-1)=1*2*1=2 (prime).
If k(7)=14=(p(max)=7)*(p(min)=2), then (7-2)*(2-1)=5*1=5 (prime).
If k(8)=15=(p(max)=5)*(p(min)=3), then (5-2)*(3-1)=3*2=6=a(4), etc.
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CROSSREFS
| Sequence in context: A093577 A065442 A198752 * A055955 A165071 A021900
Adjacent sequences: A141459 A141460 A141461 * A141463 A141464 A141465
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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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