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A173143
Partial sums of the squarefree numbers, A005117.
16
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
Sequence in context: A071619 A025735 A023601 * A109413 A294397 A003022
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 10 2010
STATUS
approved