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%I #27 Sep 08 2022 08:45:19
%S 0,-1,1,4,0,5,11,18,26,17,27,38,50,63,77,92,76,93,111,130,150,171,193,
%T 216,240,215,241,268,296,325,355,386,418,451,485,520,484,521,559,598,
%U 638,679,721,764,808,853,899,946,994,945,995,1046,1098,1151,1205,1260,1316,1373,1431,1490,1550,1611,1673,1736,1672
%N Partial sums of the positive integers n according to the rule: if n is square then subtract n, otherwise add n.
%H Harvey P. Dale, <a href="/A108174/b108174.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{i=1..n} i*(-1)^tau(i), where tau(i) = A000005(i). - _Ridouane Oudra_, Oct 08 2019
%F a(n) = (1/6)*(3*n^2 + 3*n - 2*floor(sqrt(n)) - 6*floor(sqrt(n))^2 - 4*floor(sqrt(n))^3). - _Ridouane Oudra_, Aug 22 2021
%t Accumulate[Table[If[IntegerQ[Sqrt[n]],-n,n],{n,0,70}]] (* _Harvey P. Dale_, Jan 17 2017 *)
%o (PARI) g(n) = my(s=0); for(x=0, n, if(issquare(x),s-=x,s+=x); print1(s, ", "))
%o (Magma) [0] cat [&+[i*(-1)^#Divisors(i):i in [1..n]]:n in [1..70]]; // _Marius A. Burtea_, Oct 09 2019
%Y Cf. A000005, A000290 (squares).
%K easy,sign
%O 0,4
%A _Cino Hilliard_, Jun 13 2005
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