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A141554
Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2 and the smallest prime incremented by 2.
2
0, 4, 0, 12, 8, 20, 15, 0, 12, 24, 25, 36, 16, 21, 44, 15, 40, 36, 0, 45, 60, 35, 24, 68, 55, 48, 60, 72, 45, 84, 32, 45, 60, 75, 88, 36, 63, 80, 85, 108, 72, 116, 75, 0, 77, 108, 120, 105, 100, 48, 140, 75, 136, 81, 132, 96, 45, 156, 120, 105, 164, 135, 144, 108, 99, 168
OFFSET
1,2
COMMENTS
In the prime number decomposition 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+2. If the product of this modified list of factors, k*(pmax-2)*(pmin+2)/(pmin*pmax), is nonprime, it is added to the sequence.
EXAMPLE
k(1)=4=(p(max)=2)*(p(min)=2), transformed (2-2)*(2+2)=0*4=0=a(1).
k(2)=6=(p(max)=3)*(p(min)=2), transformed (3-2)*(2+2)=1*4=4=a(2).
k(3)=8=(p(max)=2)*(p=2)*(p(min)=2), transformed (2-2)*2*(2+2)=0*2*4=0=a(3).
k(4)=9=(p(max)=3)*(p(min)=3), transformed (3-2)*(3+2)=1*5=5 (prime, skipped).
k(5)=10=(p(max)=5)*(p(min)=2), transformed (5-2)*(2+2)=3*4=12=a(4).
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited and corrected by R. J. Mathar, Aug 18 2008
STATUS
approved