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A365869
Numbers whose exponent of least prime factor in their prime factorization is even.
3
4, 9, 12, 16, 20, 25, 28, 36, 44, 45, 48, 49, 52, 60, 63, 64, 68, 76, 80, 81, 84, 92, 99, 100, 108, 112, 116, 117, 121, 124, 132, 140, 144, 148, 153, 156, 164, 169, 171, 172, 175, 176, 180, 188, 192, 196, 204, 207, 208, 212, 220, 225, 228, 236, 240, 244, 252, 256
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
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
Subsequence of A283050.
Subsequences: A365870, A365871.
Sequence in context: A337103 A312855 A348752 * A312856 A010449 A210607
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 21 2023
STATUS
approved