This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382064 #11 Mar 14 2025 21:17:04
%S A382064 1,256,432,512,648,2000,4096,5000,5184,5488,6561,6912,10125,11664,
%T A382064 16875,19208,19683,21296,27783,32000,35152,40000,41472,52488,54000,
%U A382064 62208,64827,78608,81000,87808,107811,109744,110592,117128,135000,148176,153664,177957,186624
%N A382064 Cubefull numbers whose number of coreful divisors is divisible by their number of exponential divisors.
%C A382064 Cubefull numbers k such that A049419(k) | A005361(k).
%C A382064 The primitive terms of A382063: if k is a term and m is a cubefree number that is coprime to k, then k*m is a term of A382063.
%C A382064 The asymptotic density of A382063 can be calculated using the terms of this sequence (see A382063 for a formula).
%H A382064 Amiram Eldar, <a href="/A382064/b382064.txt">Table of n, a(n) for n = 1..10000</a>
%H A382064 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%e A382064 256 = 2^8 is a term since it is cubefull, A005361(256) = 8, A049419(256) = 4, and 4 | 8.
%e A382064 432 = 2^4 * 3^3 is a term since it is cubefull, A005361(432) = 12, A049419(432) = 6, and 6 | 12.
%t A382064 q[k_] := Module[{e = FactorInteger[k][[;;, 2]]}, AllTrue[e, # > 2 &] && Divisible[Times @@ e, Times @@ DivisorSigma[0, e]]]; Select[Range[140000], # == 1 || q[#] &]
%o A382064 (PARI) isok(k) = if(k == 1, 1, my(e = factor(k)[, 2]); vecmin(e) > 2 && !(vecprod(e) % vecprod(apply(x -> numdiv(x), e))));
%Y A382064 Intersection of A036966 and A382063.
%Y A382064 Cf. A004709, A005361, A049419, A382062.
%K A382064 nonn
%O A382064 1,2
%A A382064 _Amiram Eldar_, Mar 14 2025