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A185232
n-th arithmetic derivative of n.
3
0, 0, 0, 0, 4, 0, 0, 0, 1520, 0, 0, 0, 235072, 0, 0, 705280, 278539264, 0, 0, 0, 226593936, 0, 0, 0, 295266178368, 0, 24143851798528, 27, 10557680820452065280, 0, 0, 0, 2821525007683005301391360, 0, 0, 2821525007683005301391360, 43942858408664114852524638339072
OFFSET
0,5
COMMENTS
a(n) is zero for all prime n.
LINKS
MATHEMATICA
dn[0]=0; dn[1]=0; dn[n_] := Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; Table[Nest[dn, n, n], {n, 50}]
PROG
(Python)
from sympy import factorint
def A185232(n):
for _ in range(n):
if n <= 1: return 0
n = sum((n*e//p for p, e in factorint(n).items()))
return n # Chai Wah Wu, Nov 03 2022
CROSSREFS
Cf. A003415.
Main diagonal of A258651.
Sequence in context: A258647 A013334 A258648 * A258649 A258650 A156393
KEYWORD
nonn
AUTHOR
STATUS
approved