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A258846
The pi-based arithmetic derivative of n^n.
2
0, 0, 4, 54, 1024, 9375, 326592, 3294172, 201326592, 4649045868, 110000000000, 1426558353055, 178322008965120, 1817250639553518, 166680102383370240, 8319983917236328125, 590295810358705651712, 5790681833204357349239, 1298431466484785739988992
OFFSET
0,3
LINKS
FORMULA
a(n) = A258851(A000312(n)).
a(n) = n^n * A258851(n).
a(n) = A258997(n,n).
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 *)
CROSSREFS
Main diagonal of A258997.
Sequence in context: A304556 A127833 A346291 * A093983 A242006 A259063
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 12 2015
STATUS
approved