A141466 - OEIS

%I #14 Feb 21 2021 03:32:57

%S 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,

%T 20,24,22,16,36,20,32,24,18,40,24,36,28,24,30,36,16,48,30,32,44,30,24,

%U 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

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

%C 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.

%e   composite k     transformed product

%e   -----------  -------------------------

%e    4 = 2*2     (2-1)*(2-1)   = 1*1   = 1  = a(1)

%e    6 = 2*3     (2-1)*(3-1)   = 1*2   = 2  (prime)

%e    8 = 2*2*2   (2-1)*2*(2-1) = 1*2*1 = 2  (prime)

%e    9 = 3*3     (3-1)*(3-1)   = 2*2   = 4  = a(2)

%e   10 = 2*5     (2-1)*(5-1)   = 1*4   = 4  = a(3)

%e   12 = 2*2*3   (2-1)*2*(3-1) = 1*2*2 = 4  = a(4)

%e   14 = 2*7     (2-1)*(7-1)   = 1*6   = 6  = a(5)

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Aug 08 2008

%E Definition rephrased by _R. J. Mathar_, Aug 14 2008

%E Edited by _Jon E. Schoenfield_, Feb 20 2021