OFFSET
1,1
COMMENTS
Subsequence of A283050 and first differs from it at n = 100: A283050(100) = 300 = 2^2 * 3 * 5^2 is not a term of this sequence.
Powerful numbers and nonpowerful numbers k such that 1 < A249740(k) < A277698(k), or equivalently, 1 < A006530(A057521(k)) < A020639(A055231(k)).
The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} f(p)/(p^2-p+1) = 0.32131800923..., where f(p) = Product_{primes q <= p} (q^2-q+1)/(q^2-1).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[e] > 1 && (Min[e] > 1 || Max[e[[FirstPosition[e, 1][[1]] ;; -1]]] == 1)]; Select[Range[200], q]
PROG
(PARI) is(n) = {my(e = apply(x->if(x > 1, 2, 1), factor(n)[, 2])); n > 1 && vecmax(e) > 1 && vecsort(e, , 4) == e; }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 29 2024
STATUS
approved