A185232 n-th arithmetic derivative of n.

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

Author

José María Grau Ribas, Jan 24 2012

Keywords

• nonn

Comments

a(n) is zero for all prime n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A003415.

Main diagonal of A258651.

Programs

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}]

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