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

1,2

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.

Links

Table of n, a(n) for n=1..76.

Example

  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)

Crossrefs

Sequence in context: A256416 A256417 A229630 * A171743 A295641 A171815

Adjacent sequences: A141463 A141464 A141465 * A141467 A141468 A141469

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 08 2008

Extensions

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

Edited by Jon E. Schoenfield, Feb 20 2021

Status

approved