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a(n) = Sum_{k=1..n} (A000330(n) mod k^2).
1

%I #10 May 28 2021 00:54:42

%S 0,1,7,19,16,50,106,66,174,233,144,210,501,277,504,965,984,893,1566,

%T 1946,1691,2224,2586,1694,2713,2992,2205,4055,4778,4726,4700,7142,

%U 6655,6785,7270,7949,8169,8742,10218,8874,11375,15885,14264,16933,17925,20622,17529,20599,21695,18830,21992,24273

%N a(n) = Sum_{k=1..n} (A000330(n) mod k^2).

%C Squares in this sequence include a(1) = 0, a(2) = 1, a(5) = 16 and a(11) = 144. Are there any others?

%H Robert Israel, <a href="/A344711/b344711.txt">Table of n, a(n) for n = 1..10000</a>

%e A000330(4) = 1^2 + 2^2 + 3^2 + 4^2 = 30 so a(4) = (30 mod 1^2) + (30 mod 2^2) + (30 mod 3^2) + (30 mod 4^2) = 19.

%p f:= proc(n) local M,k;

%p M:= n*(n+1)*(2*n+1)/6;

%p add(M mod k^2, k=1..n)

%p end proc:

%p map(f, [$1..100]);

%Y Cf. A000330.

%K nonn

%O 1,3

%A _J. M. Bergot_ and _Robert Israel_, May 26 2021