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%I #14 Jan 19 2021 04:02:04
%S 0,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,2,0,1,3,1,1,0,1,0,1,0,0,0,0,
%T 0,2,0,0,0,1,1,0,1,0,1,0,0,3,1,0,1,1,0,2,1,1,0,0,0,1,0,2,2,1,1,2,1,0,
%U 1,0,0,0,0,2,1,0,1,0,0,0,0,0,1,1,1,2
%N Number of times the n-th prime (=A000040(n)) occurs in A060270.
%C Each term in A060270 is either 1 or a prime number. Moreover it is known that each prime occurs only a finite number of times in A060270.
%C By excluding the terms that equal one from A060270, we observe the smallest value of A060270(n)/log(A002110(n)) in the range n = 2..1000 to be ~1.014. From this it is believed that the primes less than 0.9*log(A002110(1001))*1.014 (~ 7138) will not occur anymore in the sequence A060270 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 7138 will no longer occur in A060270.
%H A.H.M. Smeets, <a href="/A340006/b340006.txt">Table of n, a(n) for n = 1..916</a>
%H A.H.M. Smeets, <a href="/A340006/a340006_1.png">Sum_{k = 1..n} a(k) versus A000040(n)</a>
%F It seems that Sum_{k = 1..n} a(k) ~ 0.2*A000040(n)/log(log(A000040(n))).
%e The prime number 7 does not occur in A060270, and A000040(4) = 7, so a(4) = 0.
%e The prime number 11 occurs 1 time in A060270, and A000040(5) = 11, so a(5) = 1.
%Y Cf. A000040, A002110, A038711, A060270, A340007.
%Y See also A339274, A339959 (n!).
%K nonn
%O 1,21
%A _A.H.M. Smeets_, Dec 26 2020
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