A096919 Greatest prime factor of n-th product of 3 distinct primes.

5, 7, 11, 7, 13, 17, 7, 11, 19, 13, 23, 11, 11, 17, 29, 13, 31, 19, 13, 37, 23, 11, 17, 41, 17, 43, 19, 13, 47, 19, 13, 29, 31, 53, 23, 23, 59, 17, 61, 37, 17, 11, 19, 67, 29, 41, 19, 71, 13, 43, 31, 29, 73, 17, 13, 31, 47, 79, 23, 19, 83, 23, 37, 53, 89, 37, 17, 41, 97, 59

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

A096917(n)*A096918(n)*a(n) = A007304(n).

A096917(n) < A096918(n) < a(n).

a(n) = A006530(A007304(n)).

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1, 1, 1}; f1[n_]:=Min[First/@FactorInteger[n]]; f2[n_]:=Max[First/@FactorInteger[n]]; lst={}; Do[If[f[n], AppendTo[lst, f2[n]]], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 10 2010 *)

Prog

(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot, primefactors
def A096919(n):
    def f(x): return int(n+x-sum(primepi(x//(k*m))-b for a, k in enumerate(primerange(integer_nthroot(x, 3)[0]+1), 1) for b, m in enumerate(primerange(k+1, isqrt(x//k)+1), a+1)))
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    return max(primefactors(bisection(f))) # Chai Wah Wu, Aug 30 2024

Crossrefs

Cf. A006530, A007304, A096917, A096918.

Sequence in context: A076546 A167372 A023590 * A023594 A357099 A277777

Adjacent sequences: A096916 A096917 A096918 * A096920 A096921 A096922

Keyword

nonn

Author

Reinhard Zumkeller, Jul 15 2004

Status

approved