A036101 Centered cube numbers: (n+1)^23 + n^23.

1, 8388609, 94151567435, 70462887356491, 11991297699255789, 801651152008680941, 28158477563134519159, 617664557698786568055, 9453233930011206747641, 108862938119652501095929

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Can never be prime, as a(n) = (2n + 1) * (n^22 + 11n^21 + 121n^20 + 825n^19 + 4015n^18 + 14817n^17 + 43065n^16 + 101046n^15 + 194634n^14 + 311278n^13 + 416394n^12 + 467842n^11 + 442118n^10 + 350974n^9 + 233108n^8 + 128603n^7 + 58277n^6 + 21335n^5 + 6157n^4 + 1349n^3 + 211n^2 + 21n + 1). a(1) is semiprime (A001358). [Jonathan Vos Post, Aug 28 2011]

Examples

			a(2) = 1^23 + (1+1)^23 = 8388609 = 3 * 2796203, which is semiprime.
		

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. A010811, A036099, A036100.

Programs

Magma

[(n+1)^23+n^23: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

Mathematica

Total/@Partition[Range[0,20]^23,2,1] (* Harvey P. Dale, Nov 02 2023 *)