A258846 The pi-based arithmetic derivative of n^n.

0, 0, 4, 54, 1024, 9375, 326592, 3294172, 201326592, 4649045868, 110000000000, 1426558353055, 178322008965120, 1817250639553518, 166680102383370240, 8319983917236328125, 590295810358705651712, 5790681833204357349239, 1298431466484785739988992

Offset: 0

Author

Alois P. Heinz, Jun 12 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A000312, A000720, A258851.

Main diagonal of A258997.

Programs

Maple

with(numtheory):
a:= n-> n^(n+1)*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
seq(a(n), n=0..20);

Mathematica

a[n_] := n^(n+1)*Sum[i[[2]]*PrimePi[i[[1]]]/i[[1]], {i, FactorInteger[n]}];
a[0] = 0; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 24 2017, translated from Maple *)

Formula

a(n) = A258851(A000312(n)).

a(n) = n^n * A258851(n).

a(n) = A258997(n,n).