A366067 Trajectory of 578 under the map x -> A366144(x) (divide or multiply tau(x)).
578, 3468, 62424, 2996352, 359562240, 142386647040, 177698535505920, 45704355840, 61426654248960, 294847940395008000, 19688030208000, 71821934198784000, 5985161183232, 11491509471805440, 1773381091328, 978906362413056, 2443350280582987776, 265120473153536
Offset: 1
Keywords
Examples
a(1) = 578. Applying the rule in A366144, 578 has 6 divisors. 578 is not divisible by 6, so we multiply: a(2) = 578*6 = 3468. a(7) = 177698535505920, which has 3888 divisors. 177698535505920 is divisible by 3888, so we divide: a(8) = 177698535505920/3888 = 45704355840.
Links
- Neal Gersh Tolunsky, Table of n, a(n) for n = 1..960
- Neal Gersh Tolunsky, Log plot of a(1..1000).
Programs
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Mathematica
a[1] = 578; a[n_] := a[n] = a[n-1] * If[Divisible[a[n-1], d = DivisorSigma[0, a[n-1]]], 1/d, d]; Array[a, 18] (* Amiram Eldar, Sep 29 2023 *)
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Python
from itertools import islice from sympy import divisor_count def f(n): return n//dn if n%(dn:=divisor_count(n)) == 0 else n*dn def agen(x=578): # generator of terms while True: yield x; x = f(x) print(list(islice(agen(), 18))) # Michael S. Branicky, Oct 03 2023 -
Python
from math import prod from collections import Counter from itertools import islice from sympy import factorint def A366067_gen(): # generator of terms a, b = 578, Counter({2:1,17:2}) while True: yield a c = prod((e+1 for e in b.values())) if (d:=sum((Counter(factorint(e+1)) for e in b.values()),start=Counter()))<=b: a //= c b -=d else: a *= c b += d A366067_list = list(islice(A366067_gen(),20)) # Chai Wah Wu, Oct 03 2023
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