

A141465


Prime transformed products of prime factors of the composites, the largest prime decremented by 2, the smallest by 1.


0



2, 3, 2, 5, 3, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481
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OFFSET

1,1


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 pmax2 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin1. If the product of this modified set of factors, k*(pmax2)*(pmin1)/(pmin*pmax), is prime, it is appended to the sequence.


LINKS



EXAMPLE

composite k transformed product
 
4 = 2*2 (21)*(22) = 1*0 = 0 (nonprime)
6 = 2*3 (21)*(32) = 1*1 = 1 (nonprime)
8 = 2*2*2 (21)*2*(22) = 1*2*0 = 0 (nonprime)
9 = 3*3 (31)*(32) = 2*1 = 2 = a(1)
10 = 2*5 (21)*(52) = 1*3 = 3 = a(2)
12 = 2*2*3 (21)*2*(32) = 1*2*1 = 2 = a(3)
14 = 2*7 (21)*(72) = 1*5 = 5 = a(4)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



