A036093 Centered cube numbers: (n+1)^15 + n^15.

1, 32769, 14381675, 1088090731, 31591319949, 500702562701, 5217746494519, 39931933598775, 241075504183481, 1205891132094649, 5177248169415651, 19584269744002019, 66592914588677125, 206753988571902981

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Never prime nor semiprime, nor triprime, as a(n) = (2n+1) * (n^2 + n + 1) * (n^4 + 2n^3 + 4n^2 + 3n + 1) * (n^8 + 4n^7 + 30n^6 + 76n^5 + 99n^4 + 76n^3 + 35n^2 + 9n + 1). Has the nontrivial minimum 4 prime factors when n is in {1, 5, 105, ...}. - Jonathan Vos Post, Aug 27 2011

Examples

			1^15 + (1+1)^15 = 32769 = 3^2 * 11 * 331 which has the nontrivial minimum 4 prime factors (see A014613).
		

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. A036091, A036092.

Programs

Magma

[(n+1)^15+n^15: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

Mathematica

Total/@Partition[Range[0,20]^15,2,1] (* Harvey P. Dale, Apr 18 2013 *)

PARI

a(n)=(n+1)^15+n^15 \\ Charles R Greathouse IV, Aug 30 2017