

A339274


Number of times the nth prime (=A000040(n)) occurs in A033933.


3



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, 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, 4, 0, 5, 2, 6, 2, 3, 3, 0, 5, 2, 4, 2, 3, 3, 1, 3, 2
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OFFSET

1,6


COMMENTS

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.
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.


LINKS

A.H.M. Smeets, Table of n, a(n) for n = 1..283
A.H.M. Smeets, Sum_{k = 1..n} a(k) versus A000040(n)


FORMULA

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


EXAMPLE

The prime number 13 occurs 2 times in A033933, and A000040(6) = 13, so a(6) = 2.


CROSSREFS

Cf. A000040, A033932, A033933, A339959.
See also A340006, A340007 (p#).
Sequence in context: A347099 A347239 A347097 * A335156 A158785 A346243
Adjacent sequences: A339271 A339272 A339273 * A339275 A339276 A339277


KEYWORD

nonn


AUTHOR

A.H.M. Smeets, Dec 25 2020


STATUS

approved



