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Highly composite numbers that cease to be highly composite if divided by their largest prime factor.
1

%I #39 Mar 13 2023 02:54:21

%S 24,48,360,720,7560,10080,15120,20160,25200,45360,50400,332640,665280,

%T 10810800,14414400,17297280,21621600,32432400,43243200,1102701600,

%U 2205403200,27935107200,48886437600,73329656400,97772875200,146659312800,293318625600,1606268664000

%N Highly composite numbers that cease to be highly composite if divided by their largest prime factor.

%H Amiram Eldar, <a href="/A352699/b352699.txt">Table of n, a(n) for n = 1..1199</a>

%e 24 itself is highly composite, but the largest prime factor of 24 is 3, and 24/3 = 8, which is not highly composite. So 24 is a term of this sequence.

%t With[{hcn = Cases[Import["https://oeis.org/A002182/b002182.txt", "Table"], {_, _}][[;; , 2]]}, Select[hcn, FreeQ[hcn, #/FactorInteger[#][[-1, 1]]] &, 28]] (* _Amiram Eldar_, Mar 13 2023 *)

%Y Cf. A002182, A006530, A052126, A272605.

%K nonn

%O 1,1

%A _J. Lowell_, Mar 30 2022