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A085125 Even numbers which are 7-smooth.

%I A085125 #19 Jan 31 2025 11:58:07
%S A085125 2,4,6,8,10,12,14,16,18,20,24,28,30,32,36,40,42,48,50,54,56,60,64,70,
%T A085125 72,80,84,90,96,98,100,108,112,120,126,128,140,144,150,160,162,168,
%U A085125 180,192,196,200,210,216,224,240,250,252,256,270,280,288,294,300,320,324,336
%N A085125 Even numbers which are 7-smooth.
%C A085125 Equivalently, multiples of 2 with the largest prime divisor < 10.
%F A085125 From _Amiram Eldar_, Sep 23 2024: (Start)
%F A085125 a(n) = 2*A002473(n).
%F A085125 Sum_{n>=1} 1/a(n) = 35/16. (End)
%t A085125 Select[2*Range[200],FactorInteger[#][[-1,1]]<10&] (* _Harvey P. Dale_, Jul 06 2018 *)
%o A085125 (Python)
%o A085125 from sympy import integer_log
%o A085125 def A085125(n):
%o A085125     def bisection(f,kmin=0,kmax=1):
%o A085125         while f(kmax) > kmax: kmax <<= 1
%o A085125         kmin = kmax >> 1
%o A085125         while kmax-kmin > 1:
%o A085125             kmid = kmax+kmin>>1
%o A085125             if f(kmid) <= kmid:
%o A085125                 kmax = kmid
%o A085125             else:
%o A085125                 kmin = kmid
%o A085125         return kmax
%o A085125     def f(x):
%o A085125         c = n+x
%o A085125         for i in range(integer_log(x,7)[0]+1):
%o A085125             for j in range(integer_log(m:=x//7**i,5)[0]+1):
%o A085125                 for k in range(integer_log(r:=m//5**j,3)[0]+1):
%o A085125                     c -= (r//3**k).bit_length()-1
%o A085125         return c
%o A085125     return bisection(f,n,n) # _Chai Wah Wu_, Jan 31 2025
%Y A085125 Intersection of A005843 and A002473.
%Y A085125 Cf. A085126, A085127, A085128, A085129, A080194, A085131, A085132.
%K A085125 nonn,easy
%O A085125 1,1
%A A085125 _Amarnath Murthy_, Jul 06 2003
%E A085125 More terms from _David Wasserman_, Jan 28 2005
%E A085125 Offset changed by _Andrew Howroyd_, Sep 19 2024