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 1-2 of 2 results.

A036099 Centered cube numbers: (n+1)^21 + n^21.

Original entry on oeis.org

1, 2097153, 10462450355, 4408506864307, 481235204714229, 22413787798580981, 580482814723661863, 9781917900938059815, 118642361168367135017, 1109418989131512359209, 8400249944258160101211, 53405369853627861567323
Offset: 0

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Author

N. J. A. Sloane

Keywords

Comments

After a(0) always has at least 4 prime factors, because a(n) = (2n + 1) * (n^2 + n + 1) * (n^6 + 3n^5 + 9n^4 + 13n^3 + 11n^2 + 5n + 1) * (n^12 + 6n^11 + 63n^10 + 260n^9 + 643n^8 + 1078n^7 + 1275n^6 + 1078n^5 + 650n^4 + 274n^3 + 77n^2 + 13n + 1). [Jonathan Vos Post, Aug 27 2011]

References

  • B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Links

Crossrefs

Cf. A010809, A036098, A036097.

Programs

  • Magma
    [(n+1)^21+n^21: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011
  • Mathematica
    Total/@Partition[Range[0,20]^21,2,1] (* Harvey P. Dale, Jul 02 2019 *)

A036100 Centered cube numbers: (n+1)^22 + n^22.

Original entry on oeis.org

1, 4194305, 31385253913, 17623567104025, 2401777977060041, 134005889633282761, 4041442752425255185, 77696797343421194513, 1058557878478449439345, 10984770902183611232881
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Can never be prime, as a(n) = (2n^2 + 2n + 1) * (n^20 + 10n^19 + 105n^18 + 660n^17 + 2945n^16 + 9892n^15 + 25942n^14 + 54384n^13 + 92530n^12 + 128988n^11 + 148070n^10 + 140152n^9 + 109136n^8 + 69498n^7 + 35819n^6 + 14704n^5 + 4693n^4 + 1122n^3 + 189n^2 + 20n + 1). a(2) is semiprime (see A001358). [Jonathan Vos Post, Aug 17 2011]

References

  • B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Links

Crossrefs

Cf. A010810, A036098, A036099.

Programs

  • Magma
    [(n+1)^22+n^22: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011
  • Mathematica
    Total/@(Partition[Range[0,10],2,1]^22) (* Harvey P. Dale, Jun 28 2015 *)
Showing 1-2 of 2 results.

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

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