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A379093 Numbers whose factors in the canonical prime factorization neither increase weakly nor decrease weakly but are waterproof. (Terms of A379094 but not of A379097.)

%I A379093 #9 Dec 20 2024 12:41:57
%S A379093 90,126,180,252,270,350,360,378,504,525,540,550,594,650,700,702,756,
%T A379093 810,825,850,918,950,975,1026,1050,1078,1080,1100,1134,1150,1188,1242,
%U A379093 1274,1275,1300,1350,1400,1404,1425,1512,1575,1617,1620,1650,1666,1700,1725
%N A379093 Numbers whose factors in the canonical prime factorization neither increase weakly nor decrease weakly but are waterproof. (Terms of A379094 but not of A379097.)
%H A379093 Michael De Vlieger, <a href="/A379093/b379093.txt">Table of n, a(n) for n = 1..10000</a>
%p A379093 # Using functions 'isA379094' and 'is_not_waterproof' (from A379097).
%p A379093 A := select(isA379094, {seq(1..1800)}):
%p A379093 B := select(is_not_waterproof, {seq(1..1800)}):
%p A379093 A minus B;
%t A379093 nn = 1725; s = Select[Range[nn], Nor[SquareFreeQ[#], PrimePowerQ[#]] &];
%t A379093 Select[s, Function[f, And[NoneTrue[{Sort[f], ReverseSort[f]}, # == f &],
%t A379093   Total[(f //. {a___, b_, c__, d_, e___} /;
%t A379093     AllTrue[{c}, And[# < b, # < d] &] :>
%t A379093       {a, b, Sequence @@ Table[Min[b, d], {Length[{c}] } ], d, e}) - f] == 0] ]
%t A379093 [Power @@@ FactorInteger[#]] &] (* _Michael De Vlieger_, Dec 18 2024, after _Jean-François Alcover_ at A275339 *)
%Y A379093 Cf. A379094, A379095, A379096, A379097.
%K A379093 nonn
%O A379093 1,1
%A A379093 _Peter Luschny_, Dec 17 2024