This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379094 #19 Dec 20 2024 12:42:15
%S A379094 60,84,90,120,126,132,156,168,180,204,228,240,252,264,270,276,280,300,
%T A379094 312,315,336,348,350,360,372,378,408,420,440,444,456,480,492,495,504,
%U A379094 516,520,525,528,540,550,552,560,564,585,588,594,600,616,624,630,636,650
%N A379094 Numbers whose factors in the canonical prime factorization neither increase weakly nor decrease weakly.
%C A379094 A379097 is a subsequence.
%C A379094 From _Michael De Vlieger_, Dec 18 2024: (Start)
%C A379094 Proper subset of A126706.
%C A379094 Smallest powerful number is a(314) = 2700. (End)
%H A379094 Michael De Vlieger, <a href="/A379094/b379094.txt">Table of n, a(n) for n = 1..10000</a>
%e A379094 60 is a term because the factors in the canonical prime factorization are [4, 3, 5], a list that is neither increasing nor decreasing.
%e A379094 Primorials (A002110) are not terms of this sequence.
%p A379094 with(ArrayTools):
%p A379094 fact := n -> local p; [seq(p[1]^p[2], p in ifactors(n)[2])]:
%p A379094 isA379094 := proc(n) local f; f := fact(n);
%p A379094 is(not IsMonotonic(f, direction=decreasing, strict=false) and not IsMonotonic(f, direction=increasing, strict=false)) end:
%p A379094 select(isA379094, [seq(1..650)]);
%t A379094 Select[Range[650], Function[f, NoneTrue[{Sort[f], ReverseSort[f]}, # == f &]][Power @@@ FactorInteger[#]] &] (* _Michael De Vlieger_, Dec 18 2024 *)
%o A379094 (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
%Y A379094 Cf. A053585, A057714, A085232, A140831, A379097.
%K A379094 nonn
%O A379094 1,1
%A A379094 _Peter Luschny_, Dec 17 2024