A393576 Greatest common divisors of consecutive 7-smooth numbers.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 3, 3, 1, 1, 2, 2, 4, 3, 1, 2, 2, 3, 5, 1, 3, 6, 6, 2, 2, 5, 3, 4, 8, 5, 1, 2, 1, 5, 4, 3, 3, 10, 2, 6, 7, 5, 9, 3, 4, 4, 10, 6, 8, 1, 15, 3, 1, 5, 2, 4, 2, 10, 8, 6, 6, 15, 5, 4, 12

Offset

1,10

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.

Formula

a(n) = gcd(A002473(n), A002473(n+1)).

Mathematica

s = With[{n = 1000}, Union@ Flatten@ Table[2^a * 3^b * 5^c * 7^d, {a, 0, n}, {b, 0, Log[3, n/2^a]}, {c, 0, Log[5, n/(2^a * 3^b)]}, {d, 0, Log[7, n/(2^a * 3^b * 5^c)] } ] ]; MapApply[GCD, Partition[s, 2, 1] ]

Prog

(Python)
from math import gcd
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A393576(n):
    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
    return gcd(m:=bisection(f, n, n), bisection(lambda x:f(x)+1, m, m)) # Chai Wah Wu, Mar 09 2026

Crossrefs

Cf. A002473, A112752, A186711.

Sequence in context: A078401 A372673 A271381 * A396380 A086247 A116452

Adjacent sequences: A393573 A393574 A393575 * A393577 A393578 A393579

Keyword

nonn

Author

Michael De Vlieger, Feb 23 2026

Status

approved