A141466 Nonprime transformed products of prime factors of the composites, the largest and smallest prime decremented by 1.

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

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 08 2008

Keywords

• nonn

Comments

In the prime factorization 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 appended to the sequence.

Examples

			  composite k     transformed product
  -----------  -------------------------
   4 = 2*2     (2-1)*(2-1)   = 1*1   = 1  = a(1)
   6 = 2*3     (2-1)*(3-1)   = 1*2   = 2  (prime)
   8 = 2*2*2   (2-1)*2*(2-1) = 1*2*1 = 2  (prime)
   9 = 3*3     (3-1)*(3-1)   = 2*2   = 4  = a(2)
  10 = 2*5     (2-1)*(5-1)   = 1*4   = 4  = a(3)
  12 = 2*2*3   (2-1)*2*(3-1) = 1*2*2 = 4  = a(4)
  14 = 2*7     (2-1)*(7-1)   = 1*6   = 6  = a(5)
		

Extensions

Definition rephrased by R. J. Mathar, Aug 14 2008

Edited by Jon E. Schoenfield, Feb 20 2021