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

%I A329277 #22 Nov 05 2024 18:53:39
%S A329277 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,
%T A329277 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,
%U A329277 61,3,11,7,17,3,67,19,5,5,71,3,73,7,11,5,17,5,79
%N A329277 a(n) is the fixed point reached by iterating Euler's gradus function A275314 starting at n.
%t A329277 gradus[n_] := 1 + Plus @@ ((First[#] - 1) * Last[#] & /@ FactorInteger[n]); a[n_] := FixedPoint[gradus, n]; Array[a, 100] (* _Amiram Eldar_, Nov 11 2019 *)
%o A329277 (Python)
%o A329277 from gmpy2 import is_prime
%o A329277 from sympy import factorint
%o A329277 def gradus(n):
%o A329277     sum  = 0
%o A329277     factors = factorint(n)
%o A329277     for p,a in factors.items():
%o A329277         sum += (p - 1)*a
%o A329277     return sum + 1
%o A329277 if __name__ == "__main__":
%o A329277     glist = []
%o A329277     for x in range(1, 80):
%o A329277         glist.append(gradus(x))
%o A329277     while True:
%o A329277         for p in glist:
%o A329277             a = 0
%o A329277             if not is_prime(p):
%o A329277                 glist = [gradus(x) for x in glist]
%o A329277                 a = 1
%o A329277         if a == 0:
%o A329277             break
%o A329277     print(', '.join([str(x) for x in glist]))
%o A329277 (PARI) g(n) = my (f=factor(n)); 1+sum(k=1, #f~, f[k,2]*(f[k,1]-1))
%o A329277 a(n) = while (n!=n=g(n),); n \\ _Rémy Sigrist_, Dec 03 2019
%Y A329277 Cf. A275314, A329071.
%K A329277 nonn
%O A329277 1,2
%A A329277 _Daniel Hoyt_, Nov 11 2019