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 A329277 a(n) is the fixed point reached by iterating Euler's gradus function A275314 starting at n. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS MATHEMATICA gradus[n_] := 1 + Plus @@ ((First[#] - 1) * Last[#] & /@ FactorInteger[n]); a[n_] := FixedPoint[gradus, n]; Array[a, 100] (* Amiram Eldar, Nov 11 2019 *) PROG (Python 3) 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])) (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 CROSSREFS Cf. A275314, A329071. Sequence in context: A214127 A111607 A327124 * A117531 A275940 A105555 Adjacent sequences:  A329274 A329275 A329276 * A329278 A329279 A329280 KEYWORD nonn AUTHOR Daniel Hoyt, Nov 11 2019 STATUS approved

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Last modified February 29 09:35 EST 2020. Contains 332355 sequences. (Running on oeis4.)