The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #3 Jun 12 2021 20:50:32
%S 0,1,16,2195,4096,244140908,1679616,4747561789943,549755815184,
%T 150094635297261390,1000000000000,144209936106499235037680851362,
%U 1283918464548864,542800770374370513201577400,3214199700417740936754083600,2876265888493261300182938548474503919
%N a(n) = Sum_{d|n} (n-d)^sigma(n/d).
%C If p is prime, a(p) = Sum_{d|p} (p-d)^sigma(p/d) = (p-1)^(p+1).
%e a(10) = Sum_{d|10} (10-d)^sigma(10/d) = 9^18 + 8^6 + 5^3 + 0^1 = 150094635297261390.
%t Table[Sum[(n - k)^DivisorSigma[1, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 20}]
%Y Cf. A000203 (sigma).
%K nonn
%O 1,3
%A _Wesley Ivan Hurt_, Jun 12 2021