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 A339274 #41 Jan 10 2021 22:21:29
%S A339274 0,0,0,1,1,2,0,0,1,0,4,1,1,1,1,2,3,2,1,2,3,2,2,2,3,3,4,0,4,2,4,2,1,1,
%T A339274 1,1,2,2,2,1,1,0,3,3,3,2,2,1,0,4,1,2,0,2,1,3,2,4,2,2,3,4,0,4,1,3,2,2,
%U A339274 4,0,5,2,6,2,3,3,0,5,2,4,2,3,3,1,3,2
%N A339274 Number of times the n-th prime (=A000040(n)) occurs in A033933.
%C A339274 Each term in A033933 is either 1 or a prime number. Moreover it is known that each prime occurs only a finite number of times in A033933.
%C A339274 By excluding the terms that equal one from A033933, we observe the smallest value of A033933(n)/log(n!) in the range n = 3..2000 to be ~0.1552. From this it is believed that the primes less than 0.9*log(2001!)*0.1552 (~ 1846) will not occur anymore in the sequence A033933 for n > 2000; the applied factor 0.9 is a safety factor to be more or less sure that the prime numbers up to about 1846 will no longer occur in A033933.
%H A339274 A.H.M. Smeets, <a href="/A339274/b339274.txt">Table of n, a(n) for n = 1..283</a>
%H A339274 A.H.M. Smeets, <a href="/A339274/a339274_1.png">Sum_{k = 1..n} a(k) versus A000040(n)</a>
%F A339274 It seems that Sum_{k = 1..n} a(k) ~ 0.7*A000040(n)/log(log(A000040(n))).
%e A339274 The prime number 13 occurs 2 times in A033933, and A000040(6) = 13, so a(6) = 2.
%Y A339274 Cf. A000040, A033932, A033933, A339959.
%Y A339274 See also A340006, A340007 (p#).
%K A339274 nonn
%O A339274 1,6
%A A339274 _A.H.M. Smeets_, Dec 25 2020