cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A141554 Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2 and the smallest prime incremented by 2.

Original entry on oeis.org

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

Views

Author

Juri-Stepan Gerasimov, Aug 14 2008

Keywords

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.

Examples

			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

Cf. A141218, A141219, A141220, A141284.

Extensions

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

A141553 Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2 and the smallest prime incremented by 1.

Original entry on oeis.org

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
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 14 2008

Keywords

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.

Examples

			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.

Extensions

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

A141552 Transformed products of prime factors of the composites, the largest prime and smallest prime incremented by 1.

Original entry on oeis.org

9, 12, 18, 16, 18, 24, 24, 24, 36, 36, 36, 32, 36, 48, 36, 42, 48, 48, 54, 72, 48, 54, 48, 72, 60, 56, 72, 72, 72, 72, 72, 96, 64, 90, 72, 84, 108, 72, 96, 80, 90, 108, 96, 96, 144, 84, 108, 108, 96, 120, 144, 114, 120, 120, 96, 126, 144, 144, 126, 144, 108, 132, 120, 144
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 14 2008

Keywords

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+1 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin+1. The product of this modified list of factors, k*(pmax+1)*(pmin+1)/(pmin*pmax), is added to the sequence.

Examples

			k(1)=4=(p(max)=2)*(p(min)=2), transformed (2+1)*(2+1)=3*3=9=a(1).
k(2)=6=(p(max)=3)*(p(min)=2), transformed (3+1)*(2+1)=4*3=12=a(2).
k(6)=12=(p(max)=3)*(p=2)*(p(min)=2), transformed (3+1)*2*(2+1)=4*2*3=24=a(6), etc.

Crossrefs

Cf. A141218, A141219, A141220, A141284.

Extensions

Edited and corrected by R. J. Mathar, Aug 18 2008
Showing 1-3 of 3 results.

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