OFFSET
1,1
COMMENTS
Numbers k such that A067029(k) is positive and even.
The asymptotic density of terms with least prime factor prime(n) (within all the positive integers) is d(n) = (1/(prime(n)*(prime(n)+1))) * Product_{k=1..(n-1)} (1-1/prime(k)). For example, for n = 1, 2, 3, 4, 5 and 6, d(n) = 1/6, 1/24, 1/90, 1/210, 2/1155 and 8/7007.
The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.229627797346...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
4 is a term since the exponent of the prime factor 2 in the factorization 4 = 2^2 is 2, which is even.
MATHEMATICA
Select[Range[256], EvenQ[FactorInteger[#][[1, -1]]] &]
PROG
(PARI) is(n) = n > 1 && !(factor(n)[1, 2]%2);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 21 2023
STATUS
approved