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A304678 Numbers with weakly increasing prime multiplicities.

%I A304678 #18 Jan 28 2024 14:28:13
%S A304678 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,25,26,27,29,30,
%T A304678 31,32,33,34,35,36,37,38,39,41,42,43,46,47,49,50,51,53,54,55,57,58,59,
%U A304678 61,62,64,65,66,67,69,70,71,73,74,75,77,78,79,81,82,83
%N A304678 Numbers with weakly increasing prime multiplicities.
%C A304678 Complement of A112769.
%H A304678 Seiichi Manyama, <a href="/A304678/b304678.txt">Table of n, a(n) for n = 1..10000</a>
%e A304678 12 = 2*2*3 has prime multiplicities (2,1) so is not in the sequence.
%e A304678 36 = 2*2*3*3 has prime multiplicities (2,2) so is in the sequence.
%e A304678 150 = 2*3*5*5 has prime multiplicities (1,1,2) so is in the sequence.
%p A304678 q:= n-> (l-> (t-> andmap(i-> l[i, 2]<=l[i+1, 2],
%p A304678         [$1..t-1]))(nops(l)))(sort(ifactors(n)[2])):
%p A304678 select(q, [$1..120])[];  # _Alois P. Heinz_, Nov 11 2019
%t A304678 Select[Range[200],OrderedQ[FactorInteger[#][[All,2]]]&]
%t A304678 Select[Range[90],Min[Differences[FactorInteger[#][[;;,2]]]]>=0&] (* _Harvey P. Dale_, Jan 28 2024 *)
%o A304678 (PARI) isok(n) = my(vm = factor(n)[,2]); vm == vecsort(vm); \\ _Michel Marcus_, May 17 2018
%Y A304678 Cf. A001221, A001222, A071365, A112769, A130091, A133808, A133811, A242031, A304465, A304679, A304687.
%K A304678 nonn
%O A304678 1,2
%A A304678 _Gus Wiseman_, May 16 2018