|
|
A085970
|
|
Number of integers ranging from 2 to n that are not prime-powers.
|
|
17
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,10
|
|
COMMENTS
|
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
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The a(30) = 13 numbers: 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30. - Gus Wiseman, Jul 28 2022
|
|
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
|
The version not treating 1 as a prime-power is A356068.
A000688 counts factorizations into prime-powers.
A001222 counts prime-power divisors.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|