A086287 Greatest prime factor of 7-smooth numbers.

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 3, 7, 5, 2, 3, 5, 7, 3, 5, 3, 7, 5, 2, 7, 3, 5, 7, 5, 3, 7, 5, 3, 7, 5, 7, 2, 7, 3, 5, 5, 3, 7, 5, 3, 7, 5, 7, 3, 7, 5, 5, 7, 2, 5, 7, 3, 7, 5, 5, 3, 7, 7, 5, 7, 3, 7, 5, 7, 3, 7, 5, 5, 3, 7, 5, 7, 2, 5, 7, 3, 7, 5, 7, 5, 3, 7, 7, 7, 5, 5, 7, 3, 7, 5, 5, 7, 3, 7, 7, 5

Offset

1,2

Links

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

Formula

a(n) = A006530(A002473(n)).

A086286(n) <= a(n) <= 7.

Mathematica

Reap[Do[p = FactorInteger[n][[-1, 1]]; If[p < 11, Sow[p]], {n, 1, 500}] ][[2, 1]] (* Jean-François Alcover, Dec 17 2017 *)

Prog

(Python)
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A086287(n):
    if n == 1: return 1
    def f(x):
        c = n+x
        for i in range(integer_log(x, 7)[0]+1):
            for j in range(integer_log(m:=x//7**i, 5)[0]+1):
                for k in range(integer_log(r:=m//5**j, 3)[0]+1):
                    c -= (r//3**k).bit_length()
        return c
    m = bisection(f, n, n)
    if not (m&-m)^m:
        return 2
    elif not m%7:
        return 7
    elif not m%5:
        return 5
    else:
        return 3 # Chai Wah Wu, Mar 13 2026

Crossrefs

Cf. A002473, A006530, A086286.

Sequence in context: A185642 A076690 A262549 * A253236 A342257 A286516

Adjacent sequences: A086284 A086285 A086286 * A086288 A086289 A086290

Keyword

nonn

Author

Reinhard Zumkeller, Jul 15 2003

Status

approved