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%I #11 Mar 24 2017 13:47:08
%S 0,0,4,54,1024,9375,326592,3294172,201326592,4649045868,110000000000,
%T 1426558353055,178322008965120,1817250639553518,166680102383370240,
%U 8319983917236328125,590295810358705651712,5790681833204357349239,1298431466484785739988992
%N The pi-based arithmetic derivative of n^n.
%H Alois P. Heinz, <a href="/A258846/b258846.txt">Table of n, a(n) for n = 0..380</a>
%F a(n) = A258851(A000312(n)).
%F a(n) = n^n * A258851(n).
%F a(n) = A258997(n,n).
%p with(numtheory):
%p a:= n-> n^(n+1)*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
%p seq(a(n), n=0..20);
%t a[n_] := n^(n+1)*Sum[i[[2]]*PrimePi[i[[1]]]/i[[1]], {i, FactorInteger[n]}];
%t a[0] = 0; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Mar 24 2017, translated from Maple *)
%Y Cf. A000312, A000720, A258851.
%Y Main diagonal of A258997.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jun 12 2015
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