A086286 Smallest prime factor of 7-smooth numbers.

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

Offset

1,2

Links

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

Formula

a(n) = A020639(A002473(n));

a(n) <= A086287(n) <= 7.

Prog

(Python)
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A086286(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 m&1^1:
        return 2
    elif not m%3:
        return 3
    elif not m%5:
        return 5
    else:
        return 7 # Chai Wah Wu, Mar 13 2026

Crossrefs

Cf. A002473, A020639, A086287.

Sequence in context: A072591 A085308 A209190 * A272565 A378157 A135679

Adjacent sequences: A086283 A086284 A086285 * A086287 A086288 A086289

Keyword

nonn

Author

Reinhard Zumkeller, Jul 15 2003

Status

approved