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A210679
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Number of distinct prime factors <= 7 of n.
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6
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0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 1, 0, 2, 1, 1, 1, 2, 0, 3, 0, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 3, 0, 1, 2, 1, 0, 2, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 3, 0, 1, 2, 1, 1, 2, 0, 1, 1, 3, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 1, 1, 0, 3, 1, 1
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OFFSET
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1,6
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COMMENTS
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Periodic with period length 210. - Amiram Eldar, Sep 16 2023
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (-3,-5,-6,-6,-5,-3,0,3,5,6,6,5,3,1).
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FORMULA
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a(n) <= 4.
Additive with a(p^e) = 1 if p <= 7, and 0 otherwise.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 247/210. (End)
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MATHEMATICA
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Join[{0}, Table[Count[FactorInteger[n][[All, 1]], _?(#<8&)], {n, 2, 100}]] (* Harvey P. Dale, Aug 18 2021 *)
a[n_] := PrimeNu[GCD[n, 210]]; Array[a, 100] (* Amiram Eldar, Sep 16 2023 *)
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PROG
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(Haskell)
a210679 = length . takeWhile (<= 7) . a027748_row
(PARI) a(n) = omega(gcd(n, 210)); \\ Amiram Eldar, Sep 16 2023
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CROSSREFS
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Number of distinct prime factors <= p: A171182 (p=3), A178146 (p=5), this sequence (p=7).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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