cp's OEIS Frontend

A362584 Integers k > 1 such that k >= the square of the sum of their prime factors (A074373(k)).

%I A362584 #68 Jun 24 2023 13:11:59
%S A362584 243,256,270,288,300,320,324,336,360,375,378,384,400,405,420,432,441,
%T A362584 448,450,480,486,490,495,500,504,512,525,528,540,550,560,567,576,585,
%U A362584 588,594,600,616,624,625,630,640,648,650,660,672,675,686,693,700,702,704
%N A362584 Integers k > 1 such that k >= the square of the sum of their prime factors (A074373(k)).
%H A362584 Simon R Blow, <a href="/A362584/b362584.txt">Table of n, a(n) for n = 1..5000</a>
%e A362584 243 >= A001414(243)^2 = (3+3+3+3+3=15)^2 = 225 so 243 is a term.
%e A362584 800 >= A001414(800)^2 = (2+2+2+2+2+5+5=20)^2 = 400 so 800 is a term.
%p A362584 q:= n-> n>=add(i[1]*i[2], i=ifactors(n)[2])^2:
%p A362584 select(q, [$2..800])[];  # _Alois P. Heinz_, Jun 23 2023
%t A362584 Select[Range[2, 700], # >= (Plus @@ Times @@@ FactorInteger[#])^2 &] (* _Amiram Eldar_, Jun 24 2023 *)
%o A362584 (PARI) isok(n) = ((p=factor(n))[, 1]~*p[, 2])^2 <= n \\ _Thomas Scheuerle_, Jun 23 2023
%Y A362584 Cf. A001414, A074373.
%K A362584 nonn
%O A362584 1,1
%A A362584 _Simon R Blow_, Jun 23 2023