A111715 Sum of the squares of the first n squarefree numbers.

0, 1, 5, 14, 39, 75, 124, 224, 345, 514, 710, 935, 1224, 1585, 2026, 2510, 3039, 3715, 4556, 5456, 6417, 7506, 8662, 9887, 11256, 12700, 14221, 15902, 17666, 19515, 21631, 23840, 26441, 29250, 32275, 35524, 38888, 42369, 46090, 49934, 54159

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Eric Weisstein's World of Mathematics, Squarefree.

Formula

a(n) = Sum_{k=1..n} A005117(k)^2.

a(n) ~ c * n^3, where c = Pi^4/108 = 0.901936... . - Amiram Eldar, Jan 19 2024

Example

a(10) = 1^2 + 2^2 + 3^2 + 5^2 + 6^2 + 7^2 + 10^2 + 11^2 + 13^2 + 14^2 = 710.

Mathematica

Join[{0}, Accumulate[Select[Range[100], SquareFreeQ]^2]] (* Harvey P. Dale, Apr 08 2015 *)

Crossrefs

Cf. A005117.

Sequence in context: A183898 A225865 A319648 * A024525 A209536 A119996

Adjacent sequences: A111712 A111713 A111714 * A111716 A111717 A111718

Keyword

nonn,changed

Author

Jonathan Vos Post, Nov 17 2005

Status

approved