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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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-1. If the product of this modified set of factors, k*(pmax-2)*(pmin-1)/(pmin*pmax), is nonprime, it is added to the sequence.

LINKS

Table of n, a(n) for n=1..75.

EXAMPLE

If k(1)=4=(p(max)=2)*(p(min)=2), then a(1)=(2-2)*(2-1)=0*1=0 =a(1).

If k(2)=6=(p(max)=3)*(p(min)=2), then a(2)=(3-2)*(2-1)=1*1=1=a(2).

If k(3)=8=(p(max)=2)*(p=2)*(p(min)=2), then a(3)=(2-2)*2*(2-1)=0*2*1=0=a(3).

If k(4)=9=(p(max)=3)*(p(min)=3), then (3-2)*(3-1)=1*2=2 (prime).

If k(5)=10=(p(max)=5)*(p(min)=2), then (5-2)*(2-1)=3*1=3 (prime).

If k(6)=12=(p(max)=3)*(p=2)*(p(min)=2), then (3-2)*2*(2-1)=1*2*1=2 (prime).

If k(7)=14=(p(max)=7)*(p(min)=2), then (7-2)*(2-1)=5*1=5 (prime).

If k(8)=15=(p(max)=5)*(p(min)=3), then (5-2)*(3-1)=3*2=6=a(4), etc.

CROSSREFS

Sequence in context: A093577 A065442 A198752 * A055955 A165071 A223033

Adjacent sequences:  A141459 A141460 A141461 * A141463 A141464 A141465

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov Aug 08 2008

EXTENSIONS

Definition rephrased by R. J. Mathar, Aug 14 2008

STATUS

approved

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Last modified November 28 20:57 EST 2020. Contains 338755 sequences. (Running on oeis4.)