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

1,2

Links

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

Formula

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

Example

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, ...

Mathematica

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

Prog

(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

Crossrefs

Cf. A005117, A072691.

Sequence in context: A071619 A025735 A023601 * A109413 A294397 A003022

Adjacent sequences: A173140 A173141 A173142 * A173144 A173145 A173146

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 10 2010

Status

approved