A069189 - OEIS

%I #18 Oct 05 2023 18:16:56

%S 4,8,9,12,16,18,25,27,32,36,45,48,49,50,54,63,64,72,75,80,81,96,98,

%T 100,108,112,121,125,128,144,147,150,160,162,169,175,176,180,192,196,

%U 200,208,216,224,225,240,242,243,245,250,252,256,275,288,289,294,300,320

%N Numbers k such that A007913(k) < sqrt(k).

%C Equivalently, numbers k whose squarefree part, A007913(k), is smaller than their square part, A008833(k). - _Peter Munn_, Mar 26 2021

%H Amiram Eldar, <a href="/A069189/b069189.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarePart.html">Square Part</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarefreePart.html">Squarefree Part</a>.

%t f[p_, e_] := If[OddQ[e], p, 1]; sqf[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[320], sqf[#] < Sqrt[#] &] (* _Amiram Eldar_, Apr 02 2020 *)

%o (PARI) for(n=1,200,if(core(n)<sqrt(n),print1(n,",")))

%Y Cf. A007913, A008833.

%Y Subsequence of A048098.

%Y A116882 is a near equivalent with respect to a number's odd part.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Apr 10 2002