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.
%I A308904 #7 Jun 29 2019 23:04:34 %S A308904 8,20,42,84,128,184,256,332,432,534,654,784,906,1060,1226,1388,1568, %T A308904 1772,1962,2166,2420,2646,2928,3162,3424,3692,3986,4308,4630,4984, %U A308904 5296,5658,6008,6376,6750,7156,7540,7958,8388,8806,9226,9704,10170,10634,11140,11664 %N A308904 Largest number k such that exactly half the numbers in [1..k] are prime(n)-smooth. %C A308904 Cf. A290154 (Smallest number k such that exactly half the numbers in [1..k] are prime(n)-smooth). %C A308904 It appears that for most values of n, there exists more than one number k such that exactly half the numbers in [1..k] are prime(n)-smooth; see A308905. %e A308904 The 2-smooth numbers are 1, 2, 4, 8, 16, 32, ... (A000079, the powers of 2), so exactly half of the 8 numbers in the interval [1..8] are 2-smooth numbers: the 8/2 = 4 numbers 1, 2, 4, and 8. For all numbers k > 8, the number of 2-smooth numbers in [1..k] is less than k/2, so 8 is the largest k at which the number of 2-smooth numbers in [1..k] is exactly k/2, so a(1)=8. (The smallest k at which the number of 2-smooth numbers in [1..k] is exactly k/2 is A290154(1) = 6.) %e A308904 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 k=20 is the only such number, 20 is both a(2) and A290154(2). %Y A308904 Cf. A290154, A308905. %K A308904 nonn %O A308904 1,1 %A A308904 _Jon E. Schoenfield_, Jun 29 2019