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A082863
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Number of distinct prime factors of n^2-1.
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0
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1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2, 4, 2, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 2, 4, 3, 2, 4, 3, 3, 4, 3, 4, 3, 4, 2, 3, 3, 3, 4, 4, 3, 4, 2, 3, 2, 4, 3, 4, 4, 3, 3, 4, 3, 4, 4, 3, 4, 3, 3, 3, 3, 3, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| This is a very slowly growing sequence - by n=100000 the maximum value is 8. Find an asymptotic formula. Find the record holders for this sequence.
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FORMULA
| omega((n-1)*(n+1))
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EXAMPLE
| a(11)=3 because (11-1)(11+1)=10.12=2^3.3.5, which has 3 distinct prime factors, namely 2,3 and 5.
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MATHEMATICA
| Table[PrimeNu[n^2-1], {n, 2, 100}] (* From Harvey P. Dale, July 05 2011 *)
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PROG
| (PARI) for (n=2, 100, print1(omega((n-1)*(n+1))", "))
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CROSSREFS
| Sequence in context: A052298 A179938 A081412 * A029411 A165093 A066088
Adjacent sequences: A082860 A082861 A082862 * A082864 A082865 A082866
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KEYWORD
| nonn
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), May 24 2003
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