A173143 Partial sums of the squarefree numbers, A005117.

1, 3, 6, 11, 17, 24, 34, 45, 58, 72, 87, 104, 123, 144, 166, 189, 215, 244, 274, 305, 338, 372, 407, 444, 482, 521, 562, 604, 647, 693, 740, 791, 844, 899, 956, 1014, 1073, 1134, 1196, 1261, 1327, 1394, 1463, 1533, 1604, 1677, 1751, 1828, 1906, 1985, 2067, 2150

Offset: 1

Author

Jonathan Vos Post, Feb 10 2010

Keywords

• easy
• nonn

Examples

			The first squarefree numbers are: 1, 2, 3,  5,  6,  7, 10, ...
So, the first partial sums are:   1, 3, 6, 11, 17, 24, 34, ...
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A072691.

Programs

Mathematica

Accumulate[Select[Range[100],SquareFreeQ]] (* Harvey P. Dale, Jan 09 2016 *)

PARI

lista(nn)=s = 0; for (n=1, nn, if (issquarefree(n), s += n; print1(s, ", "););); \\ Michel Marcus, Oct 01 2015

PARI

helper(n,k)=my(t=(n+1)\k); binomial(t,2)*k + (n+1 - t*k)*t
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

Formula

a(n) ~ (Pi^2/12) * n^2. - Amiram Eldar, Oct 21 2020