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

1,1

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)

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A178212 A182855 A350371 * A009129 A174292 A085987

Adjacent sequences: A379091 A379092 A379093 * A379095 A379096 A379097

Keyword

nonn,new

Author

Peter Luschny, Dec 17 2024

Status

approved