A329277 a(n) is the fixed point reached by iterating Euler's gradus function A275314 starting at n.

1, 2, 3, 3, 5, 3, 7, 3, 5, 3, 11, 5, 13, 3, 7, 5, 17, 3, 19, 7, 5, 5, 23, 3, 5, 3, 7, 5, 29, 3, 31, 3, 13, 3, 11, 7, 37, 7, 7, 3, 41, 3, 43, 13, 5, 3, 47, 7, 13, 3, 19, 7, 53, 3, 7, 3, 5, 3, 59, 5, 61, 3, 11, 7, 17, 3, 67, 19, 5, 5, 71, 3, 73, 7, 11, 5, 17, 5, 79

Offset: 1

Author

Daniel Hoyt, Nov 11 2019

Keywords

• nonn

Crossrefs

Cf. A275314, A329071.

Programs

Mathematica

gradus[n_] := 1 + Plus @@ ((First[#] - 1) * Last[#] & /@ FactorInteger[n]); a[n_] := FixedPoint[gradus, n]; Array[a, 100] (* Amiram Eldar, Nov 11 2019 *)

PARI

g(n) = my (f=factor(n)); 1+sum(k=1, #f~, f[k,2]*(f[k,1]-1))
a(n) = while (n!=n=g(n),); n \\ Rémy Sigrist, Dec 03 2019

Python

from gmpy2 import is_prime
from sympy import factorint
def gradus(n):
    sum  = 0
    factors = factorint(n)
    for p,a in factors.items():
        sum += (p - 1)*a
    return sum + 1
if _name_ == "_main_":
    glist = []
    for x in range(1, 80):
        glist.append(gradus(x))
    while True:
        for p in glist:
            a = 0
            if not is_prime(p):
                glist = [gradus(x) for x in glist]
                a = 1
        if a == 0:
            break
    print(', '.join([str(x) for x in glist]))