%I #18 Aug 04 2024 03:02:17
%S 2,3,5,6,7,10,11,12,13,14,15,17,18,19,20,21,22,23,26,28,29,30,31,33,
%T 34,35,37,38,39,41,42,43,44,45,46,47,50,51,52,53,55,57,58,59,60,61,62,
%U 63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,82,83,84,85
%N Positive integers whose prime multiplicities span an initial interval of positive integers.
%C The first term in this sequence but absent from A179983 is 180.
%C The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 6, 78, 820, 8379, 84440, 846646, 8473868, 84763404, 847714834, 8477408261, ... . Apparently, the asymptotic density of this sequence exists and equals 0.8477... . - _Amiram Eldar_, Aug 04 2024
%H Amiram Eldar, <a href="/A317090/b317090.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>.
%t normalQ[m_]:=Union[m]==Range[Max[m]];
%t Select[Range[2,100],normalQ[FactorInteger[#][[All,2]]]&]
%o (PARI) is(k) = {my(e = Set(factor(k)[,2])); k > 1 && vecmax(e) == #e;} \\ _Amiram Eldar_, Aug 04 2024
%Y Cf. A001222, A007916, A055932, A056239, A069799, A112798, A124010, A133808.
%Y Cf. A317087, A317088, A317089, A317091, A317092.
%Y Subsequences: A129912\{1}, A179983\{1}.
%Y Subsequence of A337533.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jul 21 2018