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

1,2

Links

Table of n, a(n) for n=1..79.

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