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.)

90, 126, 180, 252, 270, 350, 360, 378, 504, 525, 540, 550, 594, 650, 700, 702, 756, 810, 825, 850, 918, 950, 975, 1026, 1050, 1078, 1080, 1100, 1134, 1150, 1188, 1242, 1274, 1275, 1300, 1350, 1400, 1404, 1425, 1512, 1575, 1617, 1620, 1650, 1666, 1700, 1725

Offset: 1

Author

Peter Luschny, Dec 17 2024

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A379094, A379095, A379096, A379097.

Programs

Maple

# Using functions 'isA379094' and 'is_not_waterproof' (from A379097).
A := select(isA379094, {seq(1..1800)}):
B := select(is_not_waterproof, {seq(1..1800)}):
A minus B;

Mathematica

nn = 1725; s = Select[Range[nn], Nor[SquareFreeQ[#], PrimePowerQ[#]] &];
Select[s, Function[f, And[NoneTrue[{Sort[f], ReverseSort[f]}, # == f &],
  Total[(f //. {a___, b_, c__, d_, e___} /;
    AllTrue[{c}, And[# < b, # < d] &] :>
      {a, b, Sequence @@ Table[Min[b, d], {Length[{c}] } ], d, e}) - f] == 0] ]
[Power @@@ FactorInteger[#]] &] (* Michael De Vlieger, Dec 18 2024, after Jean-François Alcover at A275339 *)