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%I #12 Oct 08 2021 23:56:28
%S 1,6,12,84,30,1374,56,4680,819,10210,132,3008748,182,38822,51090,
%T 1118480,306,34123698,380,64168820,195384,235246,552,110267095704,
%U 16275,458354,551880,482528508,870,656102432730,992,1108378656,1188132,1338682,1503110,101564312008644
%N a(n) = Sum_{d|n} n^tau(d).
%C If p is prime, a(p) = Sum_{d|p} p^tau(d) = p^1 + p^2 = p*(p + 1).
%H Seiichi Manyama, <a href="/A345271/b345271.txt">Table of n, a(n) for n = 1..10000</a>
%e a(10) = Sum_{d|10} 10^tau(d) = 10^1 + 10^2 + 10^2 + 10^4 = 10210.
%t Table[Sum[n^DivisorSigma[0, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]
%o (PARI) a(n) = sumdiv(n, d, n^numdiv(d)); \\ _Michel Marcus_, Oct 08 2021
%Y Cf. A000005 (tau), A174937, A345270, A345895.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Jun 12 2021
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