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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A308905 Number of numbers k such that exactly half the numbers in [1..k] are prime(n)-smooth.

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%I A308905 #8 Jun 29 2019 23:04:43
%S A308905 2,1,1,4,5,1,4,1,3,1,1,2,1,2,7,1,4,4,3,2,5,3,6,6,1,4,1,3,2,5,3,3,2,2,
%T A308905 2,5,4,7,8,7,2,6,5,3,13,10,1,9,2,6,3,2,8,4,4,1,11,3,3,1,7,2,4,1,1,5,4,
%U A308905 2,10,5,4,6,9,7,1,3,8,8,6,6,1,3,4,2,2,2
%N A308905 Number of numbers k such that exactly half the numbers in [1..k] are prime(n)-smooth.
%C A308905 When a(n)=1, A290154(n) = A308904(n). Values of n at which this occurs begin 2, 3, 6, 8, 10, 11, 13, 16, 25, 27, 47, 56, 60, 64, 65, 75, 81, 99, ... Do they tend to occur less frequently as n increases?
%e A308905 For n=1: prime(1)=2, and the 2-smooth numbers are 1, 2, 4, 8, 16, 32, ... (A000079, the powers of 2), so for k = 1..10, the number of 2-smooth numbers in the interval [1..k] increases as follows:
%e A308905 .
%e A308905                      Number m
%e A308905         2-smooth    of 2-smooth
%e A308905         numbers       numbers
%e A308905    k   in [1..k]     in [1..k]         m/k
%e A308905   ==  ============  ===========  ===============
%e A308905    1  {1}                1       1/1  = 1.000000
%e A308905    2  {1, 2}             2       2/2  = 1.000000
%e A308905    3  {1, 2}             2       2/3  = 0.666667
%e A308905    4  {1, 2, 4}          3       3/4  = 0.750000
%e A308905    5  {1, 2, 4}          3       3/5  = 0.600000
%e A308905    6  {1, 2, 4}          3       3/6  = 0.500000 = 1/2
%e A308905    7  {1, 2, 4}          3       3/7  = 0.428571
%e A308905    8  {1, 2, 4, 8}       4       4/8  = 0.500000 = 1/2
%e A308905    9  {1, 2, 4, 8}       4       4/9  = 0.444444
%e A308905   10  {1, 2, 4, 8}       4       4/10 = 0.400000
%e A308905 .
%e A308905 It is easy to show that, for all k > 8, fewer than half of the numbers in [1..k] are 2-smooth, so there are only 2 values of k, namely, k=6 and k=8, at which exactly half of the numbers in the interval [1..k] are 2-smooth numbers, so a(1)=2.
%e A308905 For n=2: prime(2)=3, and the 3-smooth numbers are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, ... (A003586). It can be shown that k=20 is the only number k such that exactly half of the numbers in the interval [1..k] are 3-smooth. Since there is only 1 such number k, a(2)=1.
%Y A308905 Cf. A290154, A308904.
%K A308905 nonn
%O A308905 1,1
%A A308905 _Jon E. Schoenfield_, Jun 29 2019