A141465 - OEIS

A141465

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

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 pmax-2 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-2)*(pmin-1)/(pmin*pmax), is prime, it is appended to the sequence.

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

composite k transformed product

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4 = 2*2 (2-1)*(2-2) = 1*0 = 0 (nonprime)

6 = 2*3 (2-1)*(3-2) = 1*1 = 1 (nonprime)

8 = 2*2*2 (2-1)*2*(2-2) = 1*2*0 = 0 (nonprime)

9 = 3*3 (3-1)*(3-2) = 2*1 = 2 = a(1)

10 = 2*5 (2-1)*(5-2) = 1*3 = 3 = a(2)

12 = 2*2*3 (2-1)*2*(3-2) = 1*2*1 = 2 = a(3)

14 = 2*7 (2-1)*(7-2) = 1*5 = 5 = a(4)