This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078153 #17 Oct 31 2023 12:43:26 %S A078153 0,0,0,0,2,0,5,0,6,3,10,0,15,7,9,8,22,4,24,9,21,19,32,0,35,26,30,17, %T A078153 44,11,52,24,41,37,45,12,66,46,52,22,71,27,80,43,52,60,85,14,89,56,79, %U A078153 56,101,39,89,52,94,86,117,15,122,90,85,73,118,62,139,84,116,72,145,36 %N A078153 a(n) = A051201(n) - A000203(n). %H A078153 Alois P. Heinz, <a href="/A078153/b078153.txt">Table of n, a(n) for n = 1..10000</a> %e A078153 n=15: sequence of D1 = {floor(15/j)} = {15,7,5,3,3,2,2,1,1,1,1,1,1,1,1}, Union(D1) = {15,7,5,3,2,1} = divisors(15) and {7,2}, a(15) = (15+7+5+3+2+1) - sigma(15) = 7 + 2 = 9. %t A078153 Table[Apply[Plus, Union[Table[Floor[w/j], {j, 1, w}]]] -DivisorSigma[1, w], {w, 1, 128}] %o A078153 (PARI) a(n)=my(m=(sqrtint(4*n+1)-1)\2); m*(m+1)/2+sum(k=1, n\(m+1), n\k)-sigma(n) \\ _Charles R Greathouse IV_, Feb 14 2013 %Y A078153 Cf. A051201, A000203, A055086, A000005, A078152, A076891. %K A078153 nonn,look %O A078153 1,5 %A A078153 _Labos Elemer_, Nov 27 2002