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Search: id:A068796
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| A068796 |
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Maximum k such that k consecutive integers starting at n have distinct numbers of prime factors (counted with multiplicity). |
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+0
3
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| 2, 1, 2, 2, 2, 3, 3, 2, 1, 3, 2, 3, 2, 1, 4, 3, 2, 2, 3, 2, 1, 3, 3, 2, 1, 2, 1, 2, 2, 4, 3, 2, 1, 1, 3, 3, 2, 1, 4, 3, 2, 2, 2, 1, 4, 3, 4, 3, 2, 2, 4, 4, 3, 2, 2, 2, 1, 3, 2, 5, 4, 3, 3, 4, 3, 2, 3, 2, 4, 3, 2, 4, 3, 2, 1, 2, 5, 5, 4, 4, 3, 3, 3, 2, 1, 1, 3, 2, 4, 3, 2, 2, 1, 1, 4, 3, 2, 1, 3, 3, 2, 3, 4
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The number of prime factors (counted with multiplicity) of n is bigomega(n) = A001222(n).
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EXAMPLE
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a(6)=3 because 6, 7, 8 and 9 have, respectively, 2, 1, 3 and 2 prime factors; the first 3 of these are distinct.
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MATHEMATICA
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bigomega[n_] := Plus@@Last/@FactorInteger[n]; a[n_] := For[k=1; s={bigomega[n]}, True, k++, If[MemberQ[s, z=bigomega[n+k]], Return[k], AppendTo[s, z]]]
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CROSSREFS
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Cf. A001222, A067665, A068797.
Sequence in context: A029232 A025807 A120254 this_sequence A154804 A053276 A064065
Adjacent sequences: A068793 A068794 A068795 this_sequence A068797 A068798 A068799
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KEYWORD
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nonn
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 05 2002
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