A379094 - OEIS

%I #19 Dec 20 2024 12:42:15

%S 60,84,90,120,126,132,156,168,180,204,228,240,252,264,270,276,280,300,

%T 312,315,336,348,350,360,372,378,408,420,440,444,456,480,492,495,504,

%U 516,520,525,528,540,550,552,560,564,585,588,594,600,616,624,630,636,650

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

%C A379097 is a subsequence.

%C From _Michael De Vlieger_, Dec 18 2024: (Start)

%C Proper subset of A126706.

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

%H Michael De Vlieger, <a href="/A379094/b379094.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 Primorials (A002110) are not terms of this sequence.

%p with(ArrayTools):

%p fact := n -> local p; [seq(p[1]^p[2], p in ifactors(n)[2])]:

%p isA379094 := proc(n) local f; f := fact(n);

%p is(not IsMonotonic(f, direction=decreasing, strict=false) and not IsMonotonic(f, direction=increasing, strict=false)) end:

%p select(isA379094, [seq(1..650)]);

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

%o (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 Cf. A053585, A057714, A085232, A140831, A379097.

%K nonn,new

%O 1,1

%A _Peter Luschny_, Dec 17 2024