A379094 Numbers whose factors in the canonical prime factorization neither increase weakly nor decrease weakly.

60, 84, 90, 120, 126, 132, 156, 168, 180, 204, 228, 240, 252, 264, 270, 276, 280, 300, 312, 315, 336, 348, 350, 360, 372, 378, 408, 420, 440, 444, 456, 480, 492, 495, 504, 516, 520, 525, 528, 540, 550, 552, 560, 564, 585, 588, 594, 600, 616, 624, 630, 636, 650

Offset: 1

Author

Peter Luschny, Dec 17 2024

Keywords

• nonn

Comments

A379097 is a subsequence.

From Michael De Vlieger, Dec 18 2024: (Start)

Proper subset of A126706.

Smallest powerful number is a(314) = 2700. (End)

Examples

			60 is a term because the factors in the canonical prime factorization are [4, 3, 5], a list that is neither increasing nor decreasing.
Primorials (A002110) are not terms of this sequence.
		

Links

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

Crossrefs

Cf. A053585, A057714, A085232, A140831, A379097.

Programs

Maple

with(ArrayTools):
fact := n -> local p; [seq(p[1]^p[2], p in ifactors(n)[2])]:
isA379094 := proc(n) local f; f := fact(n);
is(not IsMonotonic(f, direction=decreasing, strict=false) and not IsMonotonic(f, direction=increasing, strict=false)) end:
select(isA379094, [seq(1..650)]);

Mathematica

Select[Range[650], Function[f, NoneTrue[{Sort[f], ReverseSort[f]}, # == f &]][Power @@@ FactorInteger[#]] &] (* Michael De Vlieger, Dec 18 2024 *)

PARI

is_a379094(n) = my(C=apply(x->x[1]^x[2], Vec(factor(n)~))); vecsort(C)!=C && vecsort(C,,4)!=C \\ Hugo Pfoertner, Dec 18 2024