|
%I #16 Sep 08 2022 08:45:58
%S 1,134217729,7625731702715,18022024106966971,7468594995433310109,
%T 1030940949674393077661,66735852732611749389079,
%U 2483564001592792629551895,60567588642269318039802521,1058149737003040059690390169,14109994191499930367061460371
%N Centered cube numbers: (n+1)^27 + n^27.
%C 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).
%H Vincenzo Librandi, <a href="/A194561/b194561.txt">Table of n, a(n) for n = 0..10000</a>
%e The minimum nontrivial number of prime factors first appears at a(2) = 7625731702715 = 5 * 7 * 577 * 377604937.
%o (Magma) [(n+1)^27+n^27: n in [0..10]]; // _Vincenzo Librandi_, Sep 21 2011
%o (PARI) a(n)=(n+1)^27+n^27; \\ _Andrew Howroyd_, Feb 05 2018
%Y Cf. A122968, A194553.
%K nonn,easy
%O 0,2
%A _Jonathan Vos Post_, Aug 28 2011
%E a(8)-a(10) from _Andrew Howroyd_, Feb 05 2018
| 