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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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 *)