A370833 a(n) is the greatest prime dividing the n-th cubefree number, for n >= 2; a(1)=1.
1, 2, 3, 2, 5, 3, 7, 3, 5, 11, 3, 13, 7, 5, 17, 3, 19, 5, 7, 11, 23, 5, 13, 7, 29, 5, 31, 11, 17, 7, 3, 37, 19, 13, 41, 7, 43, 11, 5, 23, 47, 7, 5, 17, 13, 53, 11, 19, 29, 59, 5, 61, 31, 7, 13, 11, 67, 17, 23, 7, 71, 73, 37, 5, 19, 11, 13, 79, 41, 83, 7, 17, 43
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Jean-Marie De Koninck and Rafael Jakimczuk, Summing the largest prime factor over integer sequences, Revista de la Unión Matemática Argentina, Vol. 67, No. 1 (2024), pp. 27-35.
Programs
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Mathematica
s[n_] := Module[{f = FactorInteger[n]}, If[AllTrue[f[[;; , 2]], # < 3 &], f[[-1, 1]], Nothing]]; Array[s, 200] -
PARI
lista(kmax) = {my(f); print1(1, ", "); for(k = 2, kmax, f = factor(k); if(vecmax(f[, 2]) < 3, print1(f[#f~, 1], ", ")));} -
Python
from sympy import mobius, integer_nthroot, primefactors def A370833(n): def f(x): return n+x-sum(mobius(k)*(x//k**3) for k in range(1, integer_nthroot(x,3)[0]+1)) m, k = n, f(n) while m != k: m, k = k, f(k) return max(primefactors(m),default=1) # Chai Wah Wu, Aug 06 2024