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A104011
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Number of prime factors (with multiplicity) of centered dodecahedral numbers (A005904).
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1
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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, 2, 4, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 3, 5, 3, 3, 6, 3, 3, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| When a(n) = 2, n is an element of A104012: indices of centered dodecahedral numbers (A005904) which are semiprimes.
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REFERENCES
| B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
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FORMULA
| a(n) = A001222(A005904(n)). a(n) = Bigomega((2*n+1)*(5*n^2 + 5*n + 1)).
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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).
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CROSSREFS
| Cf. A001222, A005904, A104012.
Sequence in context: A138789 A116504 A186233 * A176775 A175778 A099774
Adjacent sequences: A104008 A104009 A104010 * A104012 A104013 A104014
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 24 2005
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