cp's OEIS Frontend

A365869 Numbers whose exponent of least prime factor in their prime factorization is even.

%I A365869 #12 Apr 27 2025 00:46:08
%S A365869 4,9,12,16,20,25,28,36,44,45,48,49,52,60,63,64,68,76,80,81,84,92,99,
%T A365869 100,108,112,116,117,121,124,132,140,144,148,153,156,164,169,171,172,
%U A365869 175,176,180,188,192,196,204,207,208,212,220,225,228,236,240,244,252,256
%N A365869 Numbers whose exponent of least prime factor in their prime factorization is even.
%C A365869 Numbers k such that A067029(k) is positive and even.
%C A365869 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.
%C A365869 The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.229627797346...
%H A365869 Amiram Eldar, <a href="/A365869/b365869.txt">Table of n, a(n) for n = 1..10000</a>
%e A365869 4 is a term since the exponent of the prime factor 2 in the factorization 4 = 2^2 is 2, which is even.
%t A365869 Select[Range[256], EvenQ[FactorInteger[#][[1, -1]]] &]
%o A365869 (PARI) is(n) = n > 1 && !(factor(n)[1,2]%2);
%Y A365869 Cf. A020639, A067029.
%Y A365869 Subsequence of A283050.
%Y A365869 Subsequences: A365870, A365871.
%K A365869 nonn,easy
%O A365869 1,1
%A A365869 _Amiram Eldar_, Sep 21 2023