cp's OEIS Frontend

A071604 a(n) is the number of 7-smooth numbers <= n.

%I A071604 #19 Sep 16 2024 14:25:38
%S A071604 1,2,3,4,5,6,7,8,9,10,10,11,11,12,13,14,14,15,15,16,17,17,17,18,19,19,
%T A071604 20,21,21,22,22,23,23,23,24,25,25,25,25,26,26,27,27,27,28,28,28,29,30,
%U A071604 31,31,31,31,32,32,33,33,33,33,34,34,34,35,36,36,36,36,36,36,37,37,38
%N A071604 a(n) is the number of 7-smooth numbers <= n.
%C A071604 A 7-smooth number is a number of the form 2^x*3^y*5^z*7^u, (x,y,z,u) >= 0.
%C A071604 In other words, a 7-smooth number is a number with no prime factor greater than 7. - _Peter Munn_, Nov 20 2021
%H A071604 David A. Corneth, <a href="/A071604/b071604.txt">Table of n, a(n) for n = 1..10000</a>
%F A071604 a(n) = Card{ k | A002473 (k) <= n }.
%e A071604 a(11) = 10 as there are 10 7-smooth numbers <= 11. Namely 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. - _David A. Corneth_, Apr 19 2021
%o A071604 (PARI) for(n=1,100,print1(sum(k=1,n,if(sum(i=5,n,if(k%prime(i),0,1)),0,1)),","))
%o A071604 (Python)
%o A071604 from sympy import integer_log
%o A071604 def A071604(n):
%o A071604     c = 0
%o A071604     for i in range(integer_log(n,7)[0]+1):
%o A071604         i7 = 7**i
%o A071604         m = n//i7
%o A071604         for j in range(integer_log(m,5)[0]+1):
%o A071604             j5 = 5**j
%o A071604             r = m//j5
%o A071604             for k in range(integer_log(r,3)[0]+1):
%o A071604                 c += (r//3**k).bit_length()
%o A071604     return c # _Chai Wah Wu_, Sep 16 2024
%Y A071604 Partial sums of A086299.
%Y A071604 Column 7 of A080786.
%Y A071604 Cf. A002473, A106600, A343598.
%Y A071604 Equivalent sequences with other limits on greatest prime factor: A070939 (2), A071521 (3), A071520 (5), A071523 (11), A080684 (13), A080685 (17), A080686 (19), A096300 (log n).
%K A071604 nonn,easy
%O A071604 1,2
%A A071604 _Benoit Cloitre_, Jun 02 2002
%E A071604 Name corrected by _David A. Corneth_, Apr 19 2021