OFFSET
1,1
COMMENTS
First differs from A325241 at n = 36: A325241(36) = 2^2 * 3^2 * 5 is not a term of this sequence. Also, a(71) = 360 = 2^3 * 3^2 * 5 is the least term that is not a term of A325241.
Numbers whose unordered prime signature (i.e., sorted, see A118914) ends with two consecutive integers: {..., k, k+1} for some k >= 1.
The asymptotic density of this sequence is Sum_{k >= 1, p prime} (d(k+1, p) - d(k, p))/p^(k+1) = 0.21831645263800520483..., 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
q[k_] := Module[{e = Sort[FactorInteger[k][[;; , 2]]]}, Length[e] > 1 && e[[-1]] == e[[-2]] + 1]; Select[Range[300], q]
PROG
(PARI) is(k) = {my(e = vecsort(factor(k)[, 2])); #e > 1 && e[#e] == e[#e-1] + 1; }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 16 2024
STATUS
approved