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 A385652 #12 Jul 13 2025 19:21:22
%S A385652 1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,
%T A385652 8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,
%U A385652 10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,12
%N A385652 Maximum frequency of gpf(k) for 2 <= k <= n, where gpf(k) = A006530(k) is the greatest prime factor of k.
%C A385652 The prime p is popular on the interval [2,n] if it is the greatest prime factor of a(n) numbers in that interval; see A385503.
%H A385652 Pontus von Brömssen, <a href="/A385652/b385652.txt">Table of n, a(n) for n = 2..10000</a>
%F A385652 a(n) = max_{k=2..n} A078899(k).
%e A385652 | | cumulative frequencies for gpf's |
%e A385652 n | gpf | 2 3 5 7 11 13 17 19 23 | a(n)
%e A385652 ---+-----+----------------------------------+-----
%e A385652 2 | 2 | 1 0 0 0 0 0 0 0 0 | 1
%e A385652 3 | 3 | 1 1 0 0 0 0 0 0 0 | 1
%e A385652 4 | 2 | 2 1 0 0 0 0 0 0 0 | 2
%e A385652 5 | 5 | 2 1 1 0 0 0 0 0 0 | 2
%e A385652 6 | 3 | 2 2 1 0 0 0 0 0 0 | 2
%e A385652 7 | 7 | 2 2 1 1 0 0 0 0 0 | 2
%e A385652 8 | 2 | 3 2 1 1 0 0 0 0 0 | 3
%e A385652 9 | 3 | 3 3 1 1 0 0 0 0 0 | 3
%e A385652 10 | 5 | 3 3 2 1 0 0 0 0 0 | 3
%e A385652 11 | 11 | 3 3 2 1 1 0 0 0 0 | 3
%e A385652 12 | 3 | 3 4 2 1 1 0 0 0 0 | 4
%e A385652 13 | 13 | 3 4 2 1 1 1 0 0 0 | 4
%e A385652 14 | 7 | 3 4 2 2 1 1 0 0 0 | 4
%e A385652 15 | 5 | 3 4 3 2 1 1 0 0 0 | 4
%e A385652 16 | 2 | 4 4 3 2 1 1 0 0 0 | 4
%e A385652 17 | 17 | 4 4 3 2 1 1 1 0 0 | 4
%e A385652 18 | 3 | 4 5 3 2 1 1 1 0 0 | 5
%e A385652 19 | 19 | 4 5 3 2 1 1 1 1 0 | 5
%e A385652 20 | 5 | 4 5 4 2 1 1 1 1 0 | 5
%e A385652 21 | 7 | 4 5 4 3 1 1 1 1 0 | 5
%e A385652 22 | 11 | 4 5 4 3 2 1 1 1 0 | 5
%e A385652 23 | 23 | 4 5 4 3 2 1 1 1 1 | 5
%e A385652 24 | 3 | 4 6 4 3 2 1 1 1 1 | 6
%o A385652 (Python)
%o A385652 from collections import Counter
%o A385652 from itertools import count
%o A385652 from sympy import factorint
%o A385652 def A385652_generator():
%o A385652 c = Counter()
%o A385652 M = 0
%o A385652 for n in count(2):
%o A385652 gpf = max(factorint(n))
%o A385652 c[gpf] += 1
%o A385652 if c[gpf] > M: M += 1
%o A385652 yield M
%o A385652 (PARI) gpf(n) = if (n==1,1, vecmax(factor(n)[,1])); \\ A006530
%o A385652 a(n) = my(v=vector(n, k, gpf(k)), s=Set(v)); vecmax(apply(x->#x, vector(#s, i, select(x->(x==s[i]), v)))); \\ _Michel Marcus_, Jul 06 2025
%Y A385652 Cf. A006530, A078899, A385503, A385653, A385654.
%K A385652 nonn
%O A385652 2,3
%A A385652 _Pontus von Brömssen_, Jul 06 2025