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.

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

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

Table of n, a(n) for n=1..73.

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