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Search: id:A063962
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| A063962 |
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Number of distinct prime divisors of n that are <= sqrt(n). |
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+0
1
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| 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 3, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 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, 1, 1, 0, 3, 1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 1, 3
(list; graph; listen)
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OFFSET
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1,12
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COMMENT
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For all primes p: a(p) = 0 (not marked) and for k > 1 a(p^k) = 1.
a(1) = 0 and for n > 0 a(n) is the number of marks when applying the sieve of Eratosthenes where a stage for prime p starts at p^2.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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EXAMPLE
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a(15) = a(3*5) = 1 and a(33) = a(3*11) = 2 as 5 < 3^2 < 11.
a(33)=a(3*11)=1, as 3^2=9 < 33 and 11^2=121 > 33.
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MAPLE
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with(numtheory): a:=proc(n) local c, F, f, i: c:=0: F:=factorset(n): f:=nops(F): for i from 1 to f do if F[i]^2<=n then c:=c+1 else c:=c: fi od: c; end: seq(a(n), n=1..105); (Emeric Deutsch)
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PROGRAM
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(PARI) { for (n=1, 1000, f=factor(n)~; a=0; for (i=1, length(f), if (f[1, i]^2<=n, a++, break)); write("b063962.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 04 2009]
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CROSSREFS
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A055399, A001221.
Sequence in context: A129691 A117454 A115357 this_sequence A084114 A110475 A086971
Adjacent sequences: A063959 A063960 A063961 this_sequence A063963 A063964 A063965
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 04 2001
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EXTENSIONS
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Revised definition from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 31 2006
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