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%I #17 Oct 31 2023 12:43:26
%S 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 44,11,52,24,41,37,45,12,66,46,52,22,71,27,80,43,52,60,85,14,89,56,79,
%U 56,101,39,89,52,94,86,117,15,122,90,85,73,118,62,139,84,116,72,145,36
%N a(n) = A051201(n) - A000203(n).
%H Alois P. Heinz, <a href="/A078153/b078153.txt">Table of n, a(n) for n = 1..10000</a>
%e 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 Table[Apply[Plus, Union[Table[Floor[w/j], {j, 1, w}]]] -DivisorSigma[1, w], {w, 1, 128}]
%o (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 Cf. A051201, A000203, A055086, A000005, A078152, A076891.
%K nonn,look
%O 1,5
%A _Labos Elemer_, Nov 27 2002
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