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A104011
Number of prime factors (with multiplicity) of centered dodecahedral numbers (A005904).
2
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
0,2
COMMENTS
When a(n) = 2, n is a term of A104012: indices of centered dodecahedral numbers (A005904) which are semiprimes.
LINKS
Boon K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558; author's copy.
FORMULA
a(n) = A001222(A005904(n)).
a(n) = Bigomega((2*n+1)*(5*n^2 + 5*n + 1)).
EXAMPLE
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).
MATHEMATICA
PrimeOmega[(2*n+1)*(5*n^2+5*n+1)] /. n -> Range[0, 99] (* Giovanni Resta, Jun 17 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 24 2005
EXTENSIONS
A missing term inserted by Giovanni Resta, Jun 17 2016
STATUS
approved