A036096 - OEIS

%I #17 Sep 08 2022 08:44:52

%S 1,262145,387682633,69106897225,3883416742361,105374653934041,

%T 1729973554578865,19642812107392433,168109033806481105,

%U 1150094635296999121,6559917313492231481,32183250594377475385

%N Centered cube numbers: (n+1)^18 + n^18.

%C Never prime nor semiprime, as a(n) = (2n^2 + 2n +1) * (n^4 + 2n^3 + 5n^2 + 4n +1) * (n^12 + 6n^11 + 51n^10 + 200n^9 + 480n^8 + 786n^7 + 923n^6 + 792n^5 + 495n^4 + 220n^3 + 66n^2 + 12n + 1). Triprime for n in {9, 347, 1069, 1072, ...}. - _Jonathan Vos Post_, Aug 27 2011

%D B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

%H Vincenzo Librandi, <a href="/A036096/b036096.txt">Table of n, a(n) for n = 0..10000</a>

%e 9^18 + (9+1)^18 = 1150094635296999121 = 181 * 8461 * 750988536481, the minimum nontrivial number of prime factors.

%t Total/@Partition[Range[0,20]^18,2,1] (* _Harvey P. Dale_, May 10 2022 *)

%o (Magma) [(n+1)^18+n^18: n in [0..20]]; // _Vincenzo Librandi_, Aug 28 2011

%o (PARI) a(n)=(n+1)^18+n^18 \\ _Charles R Greathouse IV_, Aug 30 2017

%Y Cf. A010806, A036094, A036095.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_