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A339959
Number of times the n-th prime (=A000040(n)) occurs in A033932.
4
0, 0, 1, 2, 2, 0, 1, 1, 2, 2, 3, 2, 1, 2, 1, 3, 1, 2, 3, 3, 1, 1, 2, 1, 5, 2, 1, 4, 1, 3, 4, 6, 1, 2, 3, 0, 1, 0, 1, 0, 0, 3, 2, 1, 1, 1, 0, 3, 4, 5, 1, 5, 5, 0, 3, 0, 0, 8, 1, 0, 5, 2, 3, 2, 1, 4, 5, 1, 1, 1, 2, 1, 2, 0, 2, 2, 3, 4, 3, 2, 0, 6, 1, 1, 4, 4
OFFSET
1,4
COMMENTS
Each term in A033932 is either 1 or a prime number. Moreover, it is known that each prime occurs only a finite number of times in A033932.
By excluding the terms that equal one from A033932, we observe the smallest value of A033933(n)/log(n!) in the range n = 2..4000 to be ~0.1399. From this it is believed that the primes less than 0.9*log(4001!)*0.1399 (~ 3676) will not occur anymore in the sequence A033932 for n > 4000; the applied factor 0.9 is a safety factor to be more or less sure that the prime numbers up to about 3676 will no longer occur in A033932 for n > 4000.
FORMULA
It seems that Sum_{k = 1..n} a(k) ~ 0.7*A000040(n)/log(log(A000040(n))).
EXAMPLE
The prime number 11 occurs 2 times in A033932, and A000040(5) = 11, so a(5) = 2.
CROSSREFS
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Dec 25 2020
STATUS
approved