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A059957
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Sum of number of distinct prime factors of n and n+1, or number of distinct prime factors of n(n+1) or of lcm(n,n+1).
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2
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1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 2, 3, 4, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 3, 4, 4, 3, 4, 3, 3, 5, 4, 3, 4, 5, 4, 3, 3, 3, 4, 4, 4, 5, 4, 3, 3, 3, 3, 4, 5, 4, 4, 4, 3, 4, 5, 4, 4, 4, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 5, 5
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OFFSET
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1,2
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COMMENTS
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If a(n)=2, then n is in A006549 (Mersenne-primes, Fermat-primes-1).
If a(n)=2, then n is in A006549, being either a Mersenne prime, a Fermat prime minus one, or n=8, corresponding to the unique solution to Catalan's equation, 3^2 = 2^3 + 1. - Gene Ward Smith, Sep 07 2006
a(n - 1), n > 2, is the number of maximal subsemigroups of the monoid of orientation-preserving partial injective mappings on a set with n elements. - Wilf A. Wilson, Jul 21 2017
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LINKS
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FORMULA
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EXAMPLE
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For n=30030, n has 6 prime factors, 30031=59*509 so a(30030)=6+2=8.
For n=30029, a(30029)=1+6=7.
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MATHEMATICA
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Table[ PrimeNu[n*(n + 1)], {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)
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PROG
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(PARI) for(n=1, 100, print1(omega(n*(n+1)), ", ")) \\ G. C. Greubel, May 13 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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