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

0,5

Comments

a(n) is zero for all prime n.

Links

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

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

Adjacent sequences: A185229 A185230 A185231 * A185233 A185234 A185235

Keyword

nonn

Author

José María Grau Ribas, Jan 24 2012

Status

approved