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 A375205 #35 Dec 06 2024 20:43:57
%S A375205 0,0,1,1,0,1,0,2,1,2,0,1,2,1,0,1,2,0,2,1,2,0,2,1,2,0,3,2,3,1,2,3,0,2,
%T A375205 1,3,2,3,1,0,4,2,4,4,3,1,2,0,4,2,3,4,1,4,3,2,4,0,1,3,4,4,2,0,4,1,3,2,
%U A375205 4,3,4,0,1,4,3,2,5,4,2,1,3,5,4,5,3
%N A375205 PrimePi(greatest prime < sqrt(Q)) - PrimePi(greatest prime factor(Q) < sqrt(Q)), with Q = A082686(n).
%C A375205 New records appear to be in consecutive numerical order, suggesting every integer should be seen in this infinite sequence. Considering a(n)=0, empirically a power fit Y=k*x^c correlates well with the "x-th" occurrence. For example, the 491st 0 value is at n=99808.
%H A375205 Bill McEachen, <a href="/A375205/b375205.txt">Table of n, a(n) for n = 1..10000</a>
%e A375205 A082686(8)=51, with square root = 7.14... so the greatest prime < 7.14 is 7, while the greatest prime factor of 51 < 7.14 is 3. The prime count from 3 to 7 is 2, so a(8)=2.
%e A375205 A082686(999)=2883 with square root = 53.69... so the greatest prime < 53.69 is 53, while the greatest prime factor of 2883 < 53.69 is 31. The prime count from 31 to 53 is 5, so a(999)=5.
%t A375205 nmax=85;q={};m=15;Until[Length[q]==nmax,If[ !PrimeQ[m]&&EvenQ[DivisorSigma[0, m]],AppendTo[q,m]];m=m+2];Table[PrimePi[NextPrime[Sqrt[q[[n]]],-1]]-PrimePi[Select[First/@FactorInteger[q[[n]]],#<Sqrt[q[[n]]]&][[-1]] ],{n,nmax}] (* _James C. McMahon_, Dec 06 2024 *)
%Y A375205 Cf. A082686.
%K A375205 nonn
%O A375205 1,8
%A A375205 _Bill McEachen_, Oct 15 2024