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 A380404 #10 Mar 31 2025 23:09:37
%S A380404 0,1,4,16,60,377,3323,42518,646580,12285485,300378113,8028681592,
%T A380404 259488951722,9414917934636,362597756958862,15397728568256861,
%U A380404 742238179325555125,40068968503380861518,2251262473065725514585,139566579946046888545036
%N A380404 Number of prime powers that do not exceed the primorial number A002110(n).
%F A380404 a(n) = Sum_{k = 1..floor(log_2(P(n)))} pi(floor(P(n)^(1/k))), where P(n) = A002110(n).
%F A380404 a(n) = A000849(n) + A380402(n).
%e A380404 Let P = A002110 and let s = A246655.
%e A380404 a(0) = 0 since P(0) = 1, and the smallest term in s is 2.
%e A380404 a(1) = 1 since P(1) = 2.
%e A380404 a(2) = 4 since P(2) = 6 and the terms in s that do not exceed 6 are {2, 3, 4, 5}.
%e A380404 a(3) = 16 since P(3) = 30; the numbers 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, and 29 are less than 30, etc.
%t A380404 Table[Sum[PrimePi[Floor[#^(1/k)]], {k, Floor@ Log2[#]}] &[Product[Prime[i], {i, n}]], {n, 0, 14}]
%Y A380404 Cf. A000849, A002110, A182908, A246655, A380402.
%K A380404 nonn,hard,more
%O A380404 0,3
%A A380404 _Michael De Vlieger_, Jan 24 2025