%I #23 Oct 21 2020 03:07:53
%S 1,3,6,11,17,24,34,45,58,72,87,104,123,144,166,189,215,244,274,305,
%T 338,372,407,444,482,521,562,604,647,693,740,791,844,899,956,1014,
%U 1073,1134,1196,1261,1327,1394,1463,1533,1604,1677,1751,1828,1906,1985,2067,2150
%N Partial sums of the squarefree numbers, A005117.
%H Charles R Greathouse IV, <a href="/A173143/b173143.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ (Pi^2/12) * n^2. - _Amiram Eldar_, Oct 21 2020
%e The first squarefree numbers are: 1, 2, 3, 5, 6, 7, 10, ...
%e So, the first partial sums are: 1, 3, 6, 11, 17, 24, 34, ...
%t Accumulate[Select[Range[100],SquareFreeQ]] (* _Harvey P. Dale_, Jan 09 2016 *)
%o (PARI) lista(nn)=s = 0; for (n=1, nn, if (issquarefree(n), s += n; print1(s, ", "););); \\ _Michel Marcus_, Oct 01 2015
%o (PARI) helper(n,k)=my(t=(n+1)\k); binomial(t,2)*k + (n+1 - t*k)*t
%o a(n)=my(s); forsquarefree(k=1,sqrtint(n), s+=moebius(k)*helper(n,k[1]^2)); s \\ _Charles R Greathouse IV_, Feb 05 2018
%Y Cf. A005117, A072691.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Feb 10 2010