A036099 - OEIS

%I #14 Sep 08 2022 08:44:52

%S 1,2097153,10462450355,4408506864307,481235204714229,

%T 22413787798580981,580482814723661863,9781917900938059815,

%U 118642361168367135017,1109418989131512359209,8400249944258160101211,53405369853627861567323

%N Centered cube numbers: (n+1)^21 + n^21.

%C After a(0) always has at least 4 prime factors, because a(n) = (2n + 1) * (n^2 + n + 1) * (n^6 + 3n^5 + 9n^4 + 13n^3 + 11n^2 + 5n + 1) * (n^12 + 6n^11 + 63n^10 + 260n^9 + 643n^8 + 1078n^7 + 1275n^6 + 1078n^5 + 650n^4 + 274n^3 + 77n^2 + 13n + 1). [_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="/A036099/b036099.txt">Table of n, a(n) for n = 0..10000</a>

%t Total/@Partition[Range[0,20]^21,2,1] (* _Harvey P. Dale_, Jul 02 2019 *)

%o (Magma) [(n+1)^21+n^21: n in [0..20]]; // _Vincenzo Librandi_, Aug 28 2011

%Y Cf. A010809, A036098, A036097.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_