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A340006
Number of times the n-th prime (=A000040(n)) occurs in A060270.
3
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, 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, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 2
OFFSET
1,21
COMMENTS
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.
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.
FORMULA
It seems that Sum_{k = 1..n} a(k) ~ 0.2*A000040(n)/log(log(A000040(n))).
EXAMPLE
The prime number 7 does not occur in A060270, and A000040(4) = 7, so a(4) = 0.
The prime number 11 occurs 1 time in A060270, and A000040(5) = 11, so a(5) = 1.
CROSSREFS
See also A339274, A339959 (n!).
Sequence in context: A181940 A356154 A261209 * A093555 A065432 A094184
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Dec 26 2020
STATUS
approved