A112757 Greatest common divisors of consecutive 5-smooth numbers.

1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 4, 1, 1, 3, 2, 4, 4, 5, 3, 2, 2, 6, 4, 8, 3, 5, 1, 9, 6, 4, 4, 12, 5, 1, 1, 9, 6, 10, 2, 18, 12, 8, 8, 9, 15, 3, 1, 2, 2, 18, 12, 20, 4, 36, 15, 3, 16, 5, 27, 18, 30, 6, 2, 4, 4, 36, 24, 25, 5, 8, 27, 45, 9, 3, 6, 32, 10, 54, 36, 60, 12, 4, 8, 8, 45, 9, 48, 15, 5

Offset

1,6

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..750 from Harvey P. Dale)

Formula

a(n) = gcd(A051037(n), A051037(n+1)).

Mathematica

GCD@@#&/@(Partition[Select[Range[2000], Max[Transpose[ FactorInteger[ #]] [[1]]]<6&], 2, 1]) (* Harvey P. Dale, Dec 24 2015 *)

Prog

(Python)
from math import gcd
from oeis_sequences.OEISsequences import bisection
def A112757(n):
    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 gcd(m:=bisection(f, n, n), bisection(lambda x:f(x)+1, m, m)) # Chai Wah Wu, Mar 09 2026

Crossrefs

Cf. A051037, A112752.

Sequence in context: A385330 A181118 A179009 * A219794 A351469 A286334

Adjacent sequences: A112754 A112755 A112756 * A112758 A112759 A112760

Keyword

nonn

Author

Reinhard Zumkeller, Sep 18 2005

Status

approved