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A141466
Nonprime transformed products of prime factors of the composites, the largest and smallest prime decremented by 1.
0
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.
EXAMPLE
composite k transformed product
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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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition rephrased by R. J. Mathar, Aug 14 2008
Edited by Jon E. Schoenfield, Feb 20 2021
STATUS
approved