%I #14 Jan 19 2021 06:27:50

%S 0,0,0,0,0,0,1,1,1,0,0,1,0,0,1,0,1,3,0,1,0,1,0,1,0,1,2,1,1,0,1,0,0,0,

%T 0,1,1,1,1,0,0,0,2,0,1,2,0,2,0,1,2,2,0,0,0,0,0,1,1,0,1,1,1,1,2,0,4,0,

%U 0,0,1,0,0,1,1,2,0,1,1,0,1,2,0,0,2,1

%N Number of times the n-th prime (=A000040(n)) occurs in A038711.

%C Each term in A038711 is either 1 or a prime number. Moreover it is known that each prime occurs only a finite number of times in A038711.

%C By excluding the terms that equal one from A038711, we observe the smallest value of A038711(n)/log(A002110(n)) in the range n = 2..1000 to be ~1.017. From this it is believed that the primes less than 0.9*log(A002110(1001))*1.017 (~ 7157) will not occur anymore in the sequence A038711 for n > 1000; the applied factor 0.9 is a safety factor to be more or less sure that the prime numbers up to about 7157 will no longer occur in A038711.

%H A.H.M. Smeets, <a href="/A340007/b340007.txt">Table of n, a(n) for n = 1..916</a>

%H A.H.M. Smeets, <a href="/A340007/a340007_1.png">Sum_{k = 1..n} a(k) versus A000040(n)</a>

%F It seems that Sum_{k = 1..n} a(k) ~ 0.7*A000040(n)/log(log(A000040(n))).

%e The prime number 17 occurs 1 time in A038711, and A000040(7) = 17, so a(7) = 1.

%e The prime number 5 does not occur in A038711, and A000040(3) = 5, so a(3) = 0.

%Y Cf. A000040, A002110, A038711, A060270, A340006.

%Y See also A339274, A339959 (n!).

%K nonn

%O 1,18

%A _A.H.M. Smeets_, Dec 26 2020