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A082863
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Number of distinct prime factors of n^2-1.
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5
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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
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OFFSET
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2,3
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COMMENTS
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This is a very slowly growing sequence - by n=100000 the maximum value is 8.
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LINKS
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FORMULA
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EXAMPLE
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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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MAPLE
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# alternative:
A082863:= n -> nops(numtheory:-factorset(n^2-1)):
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MATHEMATICA
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PROG
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(PARI) for (n=2, 100, print1(omega((n-1)*(n+1))", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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