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A057828 Number of perfect squares, k^2, where k^2 <= n and gcd(k,n) = 1. 3

%I #20 Dec 12 2017 00:51:25

%S 1,1,1,1,2,1,2,1,2,2,3,1,3,2,2,2,4,1,4,2,3,2,4,1,4,3,4,3,5,1,5,3,4,3,

%T 4,2,6,3,4,2,6,2,6,3,3,3,6,2,6,3,5,4,7,3,6,3,5,4,7,2,7,4,4,4,7,3,8,4,

%U 6,2,8,3,8,4,5,4,7,3,8,3,6,5,9,2,8,5,6,5,9,2,8,5,6,5,8,3,9,4,6,4,10,3,10,5

%N Number of perfect squares, k^2, where k^2 <= n and gcd(k,n) = 1.

%C Number of square totatives of n, i.e., number of perfect squares less than n that are coprime to n. - _Michael De Vlieger_, Dec 11 2017

%H Reinhard Zumkeller, <a href="/A057828/b057828.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Totative.html">Totative</a>.

%e Only 2 squares, 1 and 9, are <= 14 and relatively prime to 14. So a(14) = 2.

%t Table[Count[Range[Sqrt@ n]^2, _?(CoprimeQ[#, n] &)], {n, 104}]

%o (Haskell)

%o a057828 x = length $ filter ((== 1) . (gcd x)) $

%o takeWhile (<= x) $ tail a000290_list

%o -- _Reinhard Zumkeller_, Jul 22 2012

%Y Cf. A000290, A010051.

%K nonn,look

%O 1,5

%A _Leroy Quet_, Nov 08 2000

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)