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A102294
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Number of prime divisors (with multiplicity) of icosahedral numbers.
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1
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0, 3, 5, 3, 3, 5, 3, 5, 3, 4, 5, 4, 3, 7, 4, 5, 3, 5, 5, 5, 3, 6, 4, 5, 4, 5, 6, 5, 3, 11, 3, 7, 4, 5, 9, 6, 2, 6, 5, 6, 3, 5, 4, 6, 4, 6, 6, 6, 3, 6, 6, 5, 3, 7, 5, 7, 4, 4, 6, 6, 2, 8, 6, 8, 4, 6, 6, 5, 3, 6, 5, 6, 3, 5, 5, 4, 4, 7, 3, 8, 6, 6, 6, 5, 3, 6, 5, 5, 4, 8, 5, 5, 3, 8, 6, 8, 3, 7, 10, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Because the cubic factors into n time a quadratic, the icosahedral numbers can never be prime, but can be semiprime (only if n is prime and also n*(5*n^2 - 5*n + 2)/2 is prime, as with n = 31, 61, ...
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FORMULA
| a(n) = A001222(A006564(n)). Bigomega(n*(5*n^2 - 5*n + 2)/2).
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EXAMPLE
| IcosahedralNumber(13) = 5083 = 13 * 17 * 23 so Omega(IcosahedralNumber(13)) = 3.
IcosahedralNumber(37) = 123247 = 37 * 3331 so Omega(IcosahedralNumber(37)) = 2, hence the 37th Icosahedral Number is the smallest to be semiprime.
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CROSSREFS
| Cf. A001222, A006564.
Sequence in context: A092553 A112755 A126659 * A021287 A124887 A097524
Adjacent sequences: A102291 A102292 A102293 * A102295 A102296 A102297
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2005
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