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 A141467 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS FORMULA a(n) = k*(pmax+3)*(pmin-1)/(pmin*pmax), n > 1, where k=A002808(n), pmin=A056608(n), pmax=A052369(n). EXAMPLE 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) CROSSREFS Sequence in context: A109397 A133210 A324975 * A361109 A317719 A329367 Adjacent sequences: A141464 A141465 A141466 * A141468 A141469 A141470 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Aug 08 2008 EXTENSIONS Edited by R. J. Mathar, Aug 14 2008 Further edits by Jon E. Schoenfield, Feb 20 2021 STATUS approved

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Last modified March 30 04:12 EDT 2023. Contains 361603 sequences. (Running on oeis4.)