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Cubefree numbers divisible by the square of their largest prime factor.
1

%I #8 Jan 05 2024 10:13:11

%S 4,9,18,25,36,49,50,75,98,100,121,147,150,169,196,225,242,245,289,294,

%T 300,338,361,363,441,450,484,490,507,529,578,588,605,676,722,726,735,

%U 841,845,847,867,882,900,961,980,1014,1058,1083,1089,1156,1183,1210,1225

%N Cubefree numbers divisible by the square of their largest prime factor.

%H Amiram Eldar, <a href="/A368780/b368780.txt">Table of n, a(n) for n = 1..10000</a>

%H Rafael Jakimczuk, <a href="https://doi.org/10.2478/amsil-2022-0018">Some observations on the greatest prime factor of an integer</a>, Annales Mathematicae Silesianae, Vol. 37, No. 1 (2023), pp. 67-81. See Theorem 2.2, p. 71.

%t Select[Range[1500], Max[e = FactorInteger[#][[;;, 2]]] < 3 && e[[-1]] == 2 &]

%o (PARI) is(n) = {my(e = factor(n)[, 2]); n > 1 && vecmax(e) < 3 && e[#e] == 2;}

%Y Intersection of A070003 and A004709 or A067259.

%Y Cf. A006530.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jan 05 2024