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A317092 Positive integers whose prime multiplicities are weakly decreasing and span an initial interval of positive integers.

%I A317092 #15 May 28 2025 16:35:42
%S A317092 2,3,5,6,7,10,11,12,13,14,15,17,19,20,21,22,23,26,28,29,30,31,33,34,
%T A317092 35,37,38,39,41,42,43,44,45,46,47,51,52,53,55,57,58,59,60,61,62,63,65,
%U A317092 66,67,68,69,70,71,73,74,76,77,78,79,82,83,84,85,86,87,89,91,92
%N A317092 Positive integers whose prime multiplicities are weakly decreasing and span an initial interval of positive integers.
%H A317092 Rémy Sigrist, <a href="/A317092/b317092.txt">Table of n, a(n) for n = 1..25000</a>
%t A317092 normalQ[m_]:=Union[m]==Range[Max[m]];
%t A317092 Select[Range[2,100],And[normalQ[FactorInteger[#][[All,2]]],OrderedQ[Reverse[FactorInteger[#][[All,2]]]]]&]
%o A317092 (PARI) is(n) = my (f=factor(n), w=#f~); if (w==0 || f[w,2]!=1, return (0), for (k=1, w-1, if (f[k,2]!=f[k+1,2] && f[k,2]!=1+f[k+1,2], return (0))); return (1)) \\ _Rémy Sigrist_, Sep 05 2018
%Y A317092 Cf. A001222, A007916, A055932, A056239, A112798, A124010, A133808, A242031.
%Y A317092 Cf. A317087, A317088, A317089, A317090, A317091.
%K A317092 nonn
%O A317092 1,1
%A A317092 _Gus Wiseman_, Jul 21 2018