cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A317090 Positive integers whose prime multiplicities span an initial interval of positive integers.

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%I A317090 #18 Aug 04 2024 03:02:17
%S A317090 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 A317090 34,35,37,38,39,41,42,43,44,45,46,47,50,51,52,53,55,57,58,59,60,61,62,
%U A317090 63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,82,83,84,85
%N A317090 Positive integers whose prime multiplicities span an initial interval of positive integers.
%C A317090 The first term in this sequence but absent from A179983 is 180.
%C A317090 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 A317090 Amiram Eldar, <a href="/A317090/b317090.txt">Table of n, a(n) for n = 1..10000</a>
%H A317090 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>.
%t A317090 normalQ[m_]:=Union[m]==Range[Max[m]];
%t A317090 Select[Range[2,100],normalQ[FactorInteger[#][[All,2]]]&]
%o A317090 (PARI) is(k) = {my(e = Set(factor(k)[,2])); k > 1 && vecmax(e) == #e;} \\ _Amiram Eldar_, Aug 04 2024
%Y A317090 Cf. A001222, A007916, A055932, A056239, A069799, A112798, A124010, A133808.
%Y A317090 Cf. A317087, A317088, A317089, A317091, A317092.
%Y A317090 Subsequences: A129912\{1}, A179983\{1}.
%Y A317090 Subsequence of A337533.
%K A317090 nonn
%O A317090 1,1
%A A317090 _Gus Wiseman_, Jul 21 2018