

A085970


Number of numbers <= n that are not prime powers.


6



0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 20, 21, 21, 22, 23, 24, 24, 25, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 40, 41, 41, 42, 42, 43
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OFFSET

1,10


COMMENTS

a(n) = Max{k: A024619(k)<=n};
a(n) = n  A065515(n) = A085972(n)  A000720(n).
For n > 2, a(n) gives the number of duplicate eliminations performed by the Sieve of Eratosthenes when sieving the interval [2, n].  Felix Fröhlich, Dec 10 2016
Number of terms of A024619 <= n.  Felix Fröhlich, Dec 10 2016


LINKS

Felix Fröhlich, Table of n, a(n) for n = 1..10000


MATHEMATICA

With[{nn = 75}, Table[n  Count[#, k_ /; k < n]  1, {n, nn}] &@ Join[{1}, Select[Range@ nn, PrimePowerQ]]] (* Michael De Vlieger, Dec 11 2016 *)


PROG

(PARI) a(n) = my(i=0); forcomposite(c=4, n, if(!isprimepower(c), i++)); i \\ Felix Fröhlich, Dec 10 2016


CROSSREFS

Cf. A024619.
Sequence in context: A194249 A285759 A082997 * A238884 A066683 A055038
Adjacent sequences: A085967 A085968 A085969 * A085971 A085972 A085973


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Jul 06 2003


STATUS

approved



