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%I #15 Jan 01 2024 19:57:37
%S 2,4,6,10,12,16,18,22,26,30,32,38,40,44,48,54,56,62,64,70,74,78,80,88,
%T 92,96,100,106,108,116,118,124,128,132,136,146,148,152,156,164,166,
%U 174,176,182,188,192,194,204,208,214,218,224,226,234,238,246
%N Partial sums of A161841.
%H David A. Corneth, <a href="/A161842/b161842.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael Penn, <a href="https://www.youtube.com/watch?v=SEHhzkH3ZqM">This is always even??</a>, YouTube video, 2020.
%F a(n) = 2*A094820(n).
%F a(n) = Sum_{i=1..n} (1 + A008836(i))*floor(n/i)). - _Enrique Pérez Herrero_, Jul 10 2012
%F a(n) ~ (log(n) + 2*gamma - 1)*n + sqrt(n), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jul 01 2021
%o (PARI) a(n) = sum(i=1, n, floor(n/i)) + sqrtint(n) \\ _David A. Corneth_, Dec 17 2020
%o (PARI) first(n) = {my(res = vector(n), t = 0); for(i = 1, n, t+=(numdiv(i)+issquare(i)); res[i] = t ); res } \\ _David A. Corneth_, Dec 17 2020
%Y Cf. A001620, A008836, A038548, A094820, A161841.
%K nonn,easy
%O 1,1
%A _Omar E. Pol_, Jun 23 2009