A112764 Greatest prime factor of the n-th 5-smooth number.

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

Offset

1,2

Links

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

Formula

a(n) = A006530(A051037(n));

A112763(n) <= a(n) <= 5.

Mathematica

Reap[Do[p = FactorInteger[n][[-1, 1]]; If[p < 7, Sow[p]], {n, 1, 2000}] ][[2, 1]] (* Jean-François Alcover, Dec 17 2017 *)

Prog

(Magma) [1] cat [Max(PrimeDivisors(k)): k in [2..1500]| PrimeDivisors(k) subset [2, 3, 5]]; // Marius A. Burtea, Feb 07 2020
(Python)
from oeis_sequences.OEISsequences import bisection
def A112764(n):
    if n == 1: return 1
    def f(x):
        c = n+x
        i, i5 = 0, 1
        while i5<=x:
            j, j3 = 0, 1
            y = x//i5
            z = y
            while j3 <= y:
                c -= z.bit_length()
                j += 1
                j3 *= 3
                z //= 3
            i += 1
            i5 *= 5
        return c
    return 5 if not (m:=bisection(f, n, n))%5 else 3 if (m&-m)^m else 2 # Chai Wah Wu, Mar 12 2026

Crossrefs

Cf. A051037, A006530, A086411, A112756, A112763.

Sequence in context: A007967 A054494 A306252 * A108728 A331962 A302170

Adjacent sequences: A112761 A112762 A112763 * A112765 A112766 A112767

Keyword

nonn

Author

Reinhard Zumkeller, Sep 18 2005

Status

approved