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A063962 Number of distinct prime divisors of n that are <= sqrt(n). 2
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; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

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.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

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.

MAPLE

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

MATHEMATICA

Join[{0}, Table[Count[Transpose[FactorInteger[n]][[1]], _?(#<=Sqrt[n]&)], {n, 2, 110}]] (* Harvey P. Dale, Mar 26 2015 *)

PROG

(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) ) } \\ Harry J. Smith, Sep 04 2009

(Haskell)

a063962 n = length [p | p <- a027748_row n, p ^ 2 <= n]

-- Reinhard Zumkeller, Apr 05 2012

CROSSREFS

Cf. A055399, A001221.

Cf. A027748, A063962.

Sequence in context: A117454 A115357 A171182 * A084114 A294881 A110475

Adjacent sequences:  A063959 A063960 A063961 * A063963 A063964 A063965

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 04 2001

EXTENSIONS

Revised definition from Emeric Deutsch, Jan 31 2006

STATUS

approved

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Last modified November 13 23:48 EST 2019. Contains 329106 sequences. (Running on oeis4.)