A393576 - OEIS

%I #11 Mar 12 2026 06:58:12

%S 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,

%T 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,

%U 6,8,1,15,3,1,5,2,4,2,10,8,6,6,15,5,4,12

%N Greatest common divisors of consecutive 7-smooth numbers.

%H Michael De Vlieger, <a href="/A393576/b393576.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A393576/a393576.png">Log log scatterplot of a(n)</a>, n = 1..2^20.

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

%t 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] ]

%o (Python)

%o from math import gcd

%o from sympy import integer_log

%o from oeis_sequences.OEISsequences import bisection

%o def A393576(n):

%o     def f(x):

%o         c = n+x

%o         for i in range(integer_log(x,7)[0]+1):

%o             for j in range(integer_log(m:=x//7**i,5)[0]+1):

%o                 for k in range(integer_log(r:=m//5**j,3)[0]+1):

%o                     c -= (r//3**k).bit_length()

%o         return c

%o     return gcd(m:=bisection(f,n,n),bisection(lambda x:f(x)+1,m,m)) # _Chai Wah Wu_, Mar 09 2026

%Y Cf. A002473, A112752, A186711.

%K nonn

%O 1,10

%A _Michael De Vlieger_, Feb 23 2026