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

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, 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, 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

Offset: 0

Author

Jonathan Vos Post, Feb 24 2005

Keywords

• easy
• nonn

Comments

When a(n) = 2, n is a term of A104012: indices of centered dodecahedral numbers (A005904) which are semiprimes.

Examples

			a(9) = 3 because A005904(9) = 8569 = 11 * 19 * 41, which has 3 prime factors (which happen to have the same number of digits).
a(18) = 3 because A005904(18) = 63307 = 29 * 37 * 59.
a(96) = 3 because A005904(96) = 8986273 = 101 * 193 * 461.
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).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Boon K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558; author's copy.

Crossrefs

Cf. A001222, A005904, A104012.

Programs

Mathematica

PrimeOmega[(2*n+1)*(5*n^2+5*n+1)] /. n -> Range[0, 99] (* Giovanni Resta, Jun 17 2016 *)

Formula

a(n) = A001222(A005904(n)).

a(n) = Bigomega((2*n+1)*(5*n^2 + 5*n + 1)).

Extensions

A missing term inserted by Giovanni Resta, Jun 17 2016