cp's OEIS Frontend

A104011 Number of prime factors (with multiplicity) of centered dodecahedral numbers (A005904).

%I A104011 #14 Oct 11 2024 13:15:27
%S A104011 0,2,2,2,3,2,2,3,3,3,4,2,4,4,2,2,3,3,3,3,3,2,4,3,3,3,2,4,4,3,2,6,3,3,
%T A104011 4,2,2,5,3,3,6,3,4,3,2,4,4,4,3,4,3,3,4,3,2,3,3,4,5,4,3,3,4,2,5,3,3,7,
%U A104011 3,2,3,3,4,4,2,3,5,4,3,3,3,2,4,3,4,4,4,4,3,4,3,4,4,3,5,3,3,6,3,3
%N A104011 Number of prime factors (with multiplicity) of centered dodecahedral numbers (A005904).
%C A104011 When a(n) = 2, n is a term of A104012: indices of centered dodecahedral numbers (A005904) which are semiprimes.
%H A104011 Amiram Eldar, <a href="/A104011/b104011.txt">Table of n, a(n) for n = 0..10000</a>
%H A104011 Boon K. Teo and N. J. A. Sloane, <a href="https://doi.org/10.1021/ic00220a025">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985), 4545-4558; <a href="http://neilsloane.com/doc/Me117.pdf">author's copy</a>.
%F A104011 a(n) = A001222(A005904(n)).
%F A104011 a(n) = Bigomega((2*n+1)*(5*n^2 + 5*n + 1)).
%e A104011 a(9) = 3 because A005904(9) = 8569 = 11 * 19 * 41, which has 3 prime factors (which happen to have the same number of digits).
%e A104011 a(18) = 3 because A005904(18) = 63307 = 29 * 37 * 59.
%e A104011 a(96) = 3 because A005904(96) = 8986273 = 101 * 193 * 461.
%e A104011 a(126) = 5 because A005904(126) = 20242783 = 11 * 23 * 29 * 31 * 89, which has 5 prime factors (which happen to have the same number of digits).
%t A104011 PrimeOmega[(2*n+1)*(5*n^2+5*n+1)] /. n -> Range[0, 99] (* _Giovanni Resta_, Jun 17 2016 *)
%Y A104011 Cf. A001222, A005904, A104012.
%K A104011 easy,nonn
%O A104011 0,2
%A A104011 _Jonathan Vos Post_, Feb 24 2005
%E A104011 A missing term inserted by _Giovanni Resta_, Jun 17 2016