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URL: https://oeis.org/A141462

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A141462
Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2, the smallest by 1.
0
0, 1, 0, 6, 0, 6, 10, 9, 4, 12, 6, 10, 9, 0, 18, 15, 20, 6, 22, 12, 15, 18, 18, 21, 8, 30, 15, 30, 22, 9, 36, 20, 34, 27, 18, 30, 0, 44, 27, 30, 42, 25, 12, 35, 30, 34, 54, 33, 24, 18, 39, 30, 60, 54, 36, 27, 66, 42, 58, 45, 68, 16, 35, 54, 30, 45, 44, 50, 51, 18, 45, 70, 40, 51, 84
OFFSET
1,4
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 nonprime, it is a term of the sequence.
EXAMPLE
composite k transformed product
----------- -------------------------
4 = 2*2 (2-1)*(2-2) = 1*0 = 0 = a(1)
6 = 2*3 (2-1)*(3-2) = 1*1 = 1 = a(2)
8 = 2*2*2 (2-1)*2*(2-2) = 1*2*0 = 0 = a(3)
9 = 3*3 (3-1)*(3-2) = 2*1 = 2 (prime)
10 = 2*5 (2-1)*(5-2) = 1*3 = 3 (prime)
12 = 2*2*3 (2-1)*2*(3-2) = 1*2*1 = 2 (prime)
14 = 2*7 (2-1)*(7-2) = 1*5 = 5 (prime)
15 = 3*5 (3-1)*(5-2) = 2*3 = 6 = a(4)
CROSSREFS
Sequence in context: A065442 A368501 A198752 * A354330 A055955 A165071
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition rephrased by R. J. Mathar, Aug 14 2008
Example section edited by Jon E. Schoenfield, Feb 20 2021
STATUS
approved