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%I #6 Jun 12 2021 21:19:54
%S 0,1,2,7,4,30,6,107,44,98,10,2000,12,206,258,6035,16,21963,18,14664,
%T 540,542,22,3165444,424,770,6434,53384,28,544568,30,1403235,1416,1346,
%U 1718,225979931,36,1694,2010,65907940,40,2493140,42,301152,860064,2510,46,112291412012,1812
%N a(n) = Sum_{d|n} (n-d)^tau(d).
%C If p is prime, a(p) = Sum_{d|p} (p-d)^tau(d) = (p-1)^1 + 0^2 = p-1.
%e a(10) = Sum_{d|10} (10-d)^tau(d) = 9^1 + 8^2 + 5^2 + 0^4 = 9 + 64 + 25 = 98.
%t Table[Sum[(n - k)^DivisorSigma[0, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]
%Y Cf. A000005 (tau), A174937.
%K nonn
%O 1,3
%A _Wesley Ivan Hurt_, Jun 12 2021
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