A194561 Centered cube numbers: (n+1)^27 + n^27.

1, 134217729, 7625731702715, 18022024106966971, 7468594995433310109, 1030940949674393077661, 66735852732611749389079, 2483564001592792629551895, 60567588642269318039802521, 1058149737003040059690390169, 14109994191499930367061460371

Offset: 0

Author

Jonathan Vos Post, Aug 28 2011

Keywords

• nonn
• easy

Comments

These are the lowest dimension of k-dimensional centered cube numbers which not only cannot be prime, but which, after the trivial a(0), always have at least 4 prime factors, because a(n) = (2n + 1) * (n^2 + n + 1) * (n^6 + 3n^5 + 12n^4 + 19n^3 + 15n^2 + 6n + 1) * (n^18 + 9n^17 + 117n^16 + 732n^15 + 2934n^14 + 8442n^13 + 18480n^12 + 31788n^11 + 43749n^10 + 48619n^9 + 43758n^8 + 31824n^7 + 18564n^6 + 8568n^5 + 3060n^4 + 816n^3 + 153n^2 + 18n + 1).

Examples

			The minimum nontrivial number of prime factors first appears at a(2) = 7625731702715 = 5 * 7 * 577 * 377604937.
		

Links

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

Crossrefs

Cf. A122968, A194553.

Programs

Magma

[(n+1)^27+n^27: n in [0..10]]; // Vincenzo Librandi, Sep 21 2011

PARI

a(n)=(n+1)^27+n^27; \\ Andrew Howroyd, Feb 05 2018

Extensions

a(8)-a(10) from Andrew Howroyd, Feb 05 2018