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A103981
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Number of prime factors (with multiplicity) of octahedral numbers (A005900).
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1
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0, 0, 2, 1, 3, 2, 2, 3, 4, 2, 3, 5, 4, 2, 3, 3, 7, 2, 4, 2, 5, 2, 4, 2, 4, 4, 4, 3, 4, 4, 3, 2, 6, 2, 4, 4, 4, 3, 5, 3, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| When a(n) = 2, n is an element of A103982: indices of octahedral numbers (A005900) which are semiprimes.
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REFERENCES
| Conway, J. H. and Guy, R. K. The Book of Numbers. New York, Springer-Verlag, p. 50, 1996
Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Chelsea, 1952.
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LINKS
| H. K. Kim, On Regular Polytope Numbers, Journal: Proc. Amer.Math. Soc. 131 (2003), 65-75, as PDF file.
Eric Weisstein's World of Mathematics, Octahedral Number
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FORMULA
| a(n) = A001222(A005900(n)). a(n) = Bigomega((2*n^3 + n)/3).
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EXAMPLE
| a(3) = 1 because OctahedralNumber(3) = A005900(3) = 19, which is prime and thus has only one prime factor. Because the cubic polynomial for octahedral numbers factors into n time a quadratic, the octahedral numbers can never be prime after a(3) = 19.
a(4) = 3 because A005900(4) = (2*4^3 + 4)/3 = 44 = 2 * 2 * 11, which has (with multiplicity) three prime factors.
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CROSSREFS
| Cf. A001222, A005900, A103946, A103982.
Sequence in context: A066272 A058773 A122805 * A029270 A090350 A199133
Adjacent sequences: A103978 A103979 A103980 * A103982 A103983 A103984
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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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