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A382902 The largest cubefree divisor of the n-th biquadratefree number.

%I A382902 #8 Apr 09 2025 04:19:47
%S A382902 1,2,3,4,5,6,7,4,9,10,11,12,13,14,15,17,18,19,20,21,22,23,12,25,26,9,
%T A382902 28,29,30,31,33,34,35,36,37,38,39,20,41,42,43,44,45,46,47,49,50,51,52,
%U A382902 53,18,55,28,57,58,59,60,61,62,63,65,66,67,68,69,70,71,36
%N A382902 The largest cubefree divisor of the n-th biquadratefree number.
%H A382902 Amiram Eldar, <a href="/A382902/b382902.txt">Table of n, a(n) for n = 1..10000</a>
%F A382902 a(n) = A007948(A046100(n)).
%F A382902 a(n) = (A382903(n) * A046100(n)^2)^(1/3).
%F A382902 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(4)^2 * Product_{p prime} (1 - 1/p^3 + 1/p^4 - 1/p^5) = 1.01974824991243823979... .
%t A382902 f[p_, e_] := p^Min[e, 2]; s[n_] := Module[{fct = FactorInteger[n]}, If[AllTrue[fct[[;; , 2]], # < 4 &], Times @@ f @@@ fct, Nothing]]; Array[s, 100]
%o A382902 (PARI) list(lim) = {my(f); print1(1, ", "); for(k = 2, lim, f = factor(k); if(vecmax(f[, 2]) < 4, print1(prod(i = 1, #f~, f[i, 1]^min(f[i, 2], 2)), ", ")));}
%Y A382902 Cf. A046100, A007948, A013662.
%Y A382902 Similar sequences: A382903, A382904, A382905, A382906.
%K A382902 nonn,easy
%O A382902 1,2
%A A382902 _Amiram Eldar_, Apr 08 2025