A141553 - OEIS

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A141553

Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2 and the smallest prime incremented by 1.

0, 0, 4, 9, 6, 15, 12, 0, 9, 18, 20, 27, 12, 18, 33, 12, 30, 27, 0, 36, 45, 30, 18, 51, 44, 36, 45, 54, 36, 63, 24, 40, 45, 60, 66, 27, 54, 60, 68, 81, 54, 87, 60, 0, 66, 81, 90, 84, 75, 36, 105, 60, 102, 72, 99, 72, 36, 117, 90, 90, 123, 108, 108, 81, 88, 126, 116, 135, 102, 48

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OFFSET

1,3

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 list 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..70.

EXAMPLE

k(1)=(p(max)=2)*(p(min)=2), transformed (2-2)*(2+1)=0*3=0=a(1).

k(2)=(p(max)=3)*(p(min)=2), transformed (3-2)*(2+1)=1*3=3 (prime, skipped).

k(3)=(p(max)=2)*(p=2)*(p(min)=2), transformed (2-2)*2*(2+1)=0*2*3=0=a(2), etc.

CROSSREFS

Cf. A141218, A141219, A141220, A141284.

Sequence in context: A261023 A171095 A075065 * A095065 A061207 A362436

Adjacent sequences: A141550 A141551 A141552 * A141554 A141555 A141556

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Aug 14 2008

EXTENSIONS

Edited and corrected by R. J. Mathar, Aug 18 2008

STATUS

approved