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A141467
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a(1)=1; for n > 1, a(n) is the product of prime factors of the n-th composite, but with the largest prime incremented by 3 and the smallest decremented by 1.
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0
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1, 6, 10, 12, 8, 12, 10, 16, 20, 18, 16, 20, 14, 24, 32, 16, 36, 20, 24, 40, 28, 20, 40, 36, 22, 32, 32, 30, 28, 48, 26, 48, 60, 40, 40, 32, 54, 56, 40, 44, 32, 48, 34, 60, 80, 64, 42, 40, 52, 50, 72, 40, 80, 44, 84, 48, 64, 108, 44, 60, 80, 46, 64, 56, 72, 96, 52, 68, 50, 88, 96, 70, 84
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OFFSET
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1,2
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COMMENTS
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In the prime number decomposition of k=A002808(n), one instance of the largest prime, pmax=A052369(n), is replaced by pmax+3 and one instance of the smallest prime, pmin=A056608(n), is replaced by pmin-1. a(n) is the product of this modified set of factors if nonprime. The case of n=1, k=4, is the only case where this modified product (2+3)*(2-1)=5 is prime and listed as a(1)=1.
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LINKS
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Table of n, a(n) for n=1..73.
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FORMULA
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a(n) = k*(pmax+3)*(pmin-1)/(pmin*pmax), n > 1, where k=A002808(n), pmin=A056608(n), pmax=A052369(n).
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EXAMPLE
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n-th composite
n & factorization transformed product
- --------------- --------------------------
1 4 = 2*2 (2-1)*(2+3) = 1*5 = 5 (prime)
2 6 = 2*3 (2-1)*(3+3) = 1*6 = 6 = a(2)
3 8 = 2*2*2 (2-1)*2*(2+3) = 1*2*5 = 10 = a(3)
4 9 = 3*3 (3-1)*(3+3) = 2*6 = 12 = a(4)
5 10 = 2*5 (2-1)*(5+3) = 1*8 = 8 = a(5)
6 12 = 2*2*3 (2-1)*2*(3+3) = 1*2*6 = 12 = a(6)
7 14 = 2*7 (2-1)*(7+3) = 1*10 = 10 = a(7)
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CROSSREFS
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Sequence in context: A109397 A133210 A324975 * A361109 A317719 A329367
Adjacent sequences: A141464 A141465 A141466 * A141468 A141469 A141470
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov, Aug 08 2008
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EXTENSIONS
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Edited by R. J. Mathar, Aug 14 2008
Further edits by Jon E. Schoenfield, Feb 20 2021
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STATUS
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approved
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