OFFSET
1,1
COMMENTS
First differs from A059404 at n = 55: A059404(55) = 180 = 2^2 * 3^2 * 5 is not a term of this sequence.
Numbers whose unordered prime signature (i.e., sorted, see A118914) ends with two different integers: {..., k, m} for some 1 <= k < m.
All the factorial numbers above 6 are terms.
The asymptotic density of this sequence is Sum_{k >= 1, p prime} (d(k+1, p) - d(k, p))/((p-1)*p^k) = 0.3660366524547281232052..., where d(k, p) = 0 for k = 1, and (1-1/p)/((1-1/p^k)*zeta(k)) for k > 1, is the density of terms that have in their prime factorization a prime p with the largest exponent that is > k.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
Select[Range[2, 200], Length[e = FactorInteger[#][[;; , 2]]] > 1 && Count[e, Max[e]] == 1 &]
PROG
(PARI) is(k) = if (k == 1, 0, my(e = vecsort(factor(k)[, 2])); #e > 1 && e[#e] > e[#e-1]);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 17 2024
STATUS
approved