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

243, 256, 270, 288, 300, 320, 324, 336, 360, 375, 378, 384, 400, 405, 420, 432, 441, 448, 450, 480, 486, 490, 495, 500, 504, 512, 525, 528, 540, 550, 560, 567, 576, 585, 588, 594, 600, 616, 624, 625, 630, 640, 648, 650, 660, 672, 675, 686, 693, 700, 702, 704

Offset: 1

Author

Simon R Blow, Jun 23 2023

Keywords

• nonn

Examples

			243 >= A001414(243)^2 = (3+3+3+3+3=15)^2 = 225 so 243 is a term.
800 >= A001414(800)^2 = (2+2+2+2+2+5+5=20)^2 = 400 so 800 is a term.
		

Links

• Simon R Blow, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001414, A074373.

Programs

Maple

q:= n-> n>=add(i[1]*i[2], i=ifactors(n)[2])^2:
select(q, [$2..800])[];  # Alois P. Heinz, Jun 23 2023

Mathematica

Select[Range[2, 700], # >= (Plus @@ Times @@@ FactorInteger[#])^2 &] (* Amiram Eldar, Jun 24 2023 *)

PARI

isok(n) = ((p=factor(n))[, 1]~*p[, 2])^2 <= n \\ Thomas Scheuerle, Jun 23 2023