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Partial sums of the cubefree numbers.
1

%I #20 Jan 02 2024 07:45:54

%S 1,3,6,10,15,21,28,37,47,58,70,83,97,112,129,147,166,186,207,229,252,

%T 277,303,331,360,390,421,454,488,523,559,596,634,673,714,756,799,843,

%U 888,934,981,1030,1080,1131,1183,1236,1291,1348,1406,1465,1525,1586,1648,1711

%N Partial sums of the cubefree numbers.

%C First differs from A025706 and A025730 at n = 14.

%C The analogous sequence with squarefree numbers is A173143.

%H Amiram Eldar, <a href="/A358038/b358038.txt">Table of n, a(n) for n = 1..10000</a>

%H Zhu Weiyi, <a href="https://fs.unm.edu/SNJ/OnTheCubeFreeNumberSequence.pdf">On the cube free number sequences</a>, Smarandache Notions J., Vol. 14 (2004), pp. 199-202.

%F a(n) = Sum_{k=1..n} A004709(k).

%F a(n) = (zeta(3)/2)*n^2 + O(n^(3/2+eps)) (Weiyi, 2004).

%t Accumulate[Select[Range[100], Max[FactorInteger[#][[;; , 2]]] < 3 &]]

%Y Cf. A002117, A004709, A173143.

%Y Cf. A025706, A025730.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 29 2022

%E Corrected by _Amiram Eldar_, Jan 02 2024