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.

A127990 Largest prime factor of 2*n^3 - 2*n + 9.

Original entry on oeis.org

3, 7, 19, 43, 83, 13, 227, 113, 23, 17, 883, 37, 1459, 1823, 2243, 389, 11, 431, 13, 5323, 6163, 373, 89, 9203, 103, 83, 257, 443, 439, 367, 19843, 73, 647, 26183, 9521, 797, 1607, 36559, 3593, 42643, 2417, 49367, 1709, 53, 173, 7207, 1609, 73699, 163, 7573
Offset: 1

Views

Author

Artur Jasinski, Feb 10 2007

Keywords

Comments

All numbers generated by the irreducible polynomial 2*n^3 - 2*n + 9 (A127989) are odd and composite. Smallest prime factor A127991, number of prime factors A127992

Links

Crossrefs

Cf. A006530, A127989, A127991, A127992.

Programs

  • Mathematica
    a = {}; Do[AppendTo[a, 2n^3 - 2n + 9], {n, 1, 300}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[Length[c]]]; AppendTo[b, d[[1]]], {n, 1, Length[a]}]; b

Formula

a(n) = A006530(A127989(n)). - Amiram Eldar, Mar 13 2020

A127992 Number of distinct prime factors of 2*n^3 - 2*n + 9.

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 2, 4, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 4, 3, 2, 3, 2, 4, 3, 4, 3, 2, 2, 3, 2, 2, 4, 2, 3, 4, 3, 3, 3, 4, 3, 2, 2, 2, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 2, 2, 2, 3, 3, 3, 4, 3, 4, 2, 3, 2, 2, 3, 3, 3, 2, 4, 3, 2, 3, 4, 2, 3, 2, 4
Offset: 1

Views

Author

Artur Jasinski, Feb 10 2007

Keywords

Comments

All numbers generated by the irreducible polynomial 2n^3 - 2n + 9 (A127989) are odd multiples of 3.

Links

Crossrefs

Cf. A001221, A127989, A127990 (largest prime factor), A127992 (number of prime factors).

Programs

  • Mathematica
    a = {}; Do[AppendTo[a, 2n^3 - 2n + 9], {n, 1, 300}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = Length[c]; AppendTo[b, d], {n, 1, Length[a]}]; b
Table[PrimeNu[2n^3-2n+9],{n,120}] (* Harvey P. Dale, Sep 24 2021 *)
  • PARI
    a(n)=omega(2*n^3 - 2*n + 9) \\ Charles R Greathouse IV, Mar 13 2020

Formula

a(n) = A001221(A127989(n)). - Amiram Eldar, Mar 13 2020

A127991 2*n^3 - 2*n + 9 divided by 3*largest prime factor.

Original entry on oeis.org

1, 1, 1, 1, 1, 11, 1, 3, 21, 39, 1, 31, 1, 1, 1, 7, 297, 9, 351, 1, 1, 19, 91, 1, 101, 141, 51, 33, 37, 49, 1, 299, 37, 1, 3, 39, 21, 1, 11, 1, 19, 1, 31, 1071, 351, 9, 43, 1, 481, 11, 511, 83, 3, 3, 69, 1, 1, 91, 1, 19, 187, 39, 219, 417, 553, 37, 1, 1, 1, 1369, 117, 693, 423, 31
Offset: 1

Views

Author

Artur Jasinski, Feb 10 2007

Keywords

Links

Crossrefs

Cf. A127979, A127990, A127992.

Programs

  • Mathematica
    a = {}; Do[AppendTo[a, 2n^3 - 2n + 9], {n, 1, 300}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[Length[c]]]; AppendTo[b, a[[n]]/(3 d[[1]])], {n, 1, Length[a]}]; b
  • PARI
    gpf(n)=my(f=factor(n)[,1]); if(n==1,1,f[#f]);
a(n)=my(m=2*n^3-2*n+9); m/gpf(m)/3 \\ Charles R Greathouse IV, Mar 13 2020

Formula

a(n) = A127989(n)/(3*A006530(A127989(n))). - Amiram Eldar, Mar 13 2020
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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