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A356193 a(n) is the smallest cubefull number (A036966) that is a multiple of n.

%I A356193 #18 Sep 01 2023 02:55:25
%S A356193 1,8,27,8,125,216,343,8,27,1000,1331,216,2197,2744,3375,16,4913,216,
%T A356193 6859,1000,9261,10648,12167,216,125,17576,27,2744,24389,27000,29791,
%U A356193 32,35937,39304,42875,216,50653,54872,59319,1000,68921,74088,79507,10648,3375,97336
%N A356193 a(n) is the smallest cubefull number (A036966) that is a multiple of n.
%C A356193 First differs from A053149 and A356192 at n=16.
%H A356193 Amiram Eldar, <a href="/A356193/b356193.txt">Table of n, a(n) for n = 1..10000</a>
%F A356193 Multiplicative with a(p^e) = p^max(e,3).
%F A356193 a(n) = n iff n is in A036966.
%F A356193 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + (3*p-2)/(p^3*(p-1))) = 1.76434793373691907811... . - _Amiram Eldar_, Jul 29 2022
%F A356193 Sum_{k=1..n} a(k) ~ c * n^4, where c = (zeta(3)/4) * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 2/p^5 - 1/p^6 - 1/p^8 + 2/p^9 - 1/p^10) = 0.1559111567... . - _Amiram Eldar_, Nov 13 2022
%F A356193 a(n) = n * A360541(n). - _Amiram Eldar_, Sep 01 2023
%t A356193 f[p_, e_] := p^Max[e, 3]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50]
%o A356193 (PARI) a(n) = {my(f=factor(n)); prod(i=1, #f~, f[i,1]^max(f[i,2],3))};
%Y A356193 Cf. A002117, A036966, A360541.
%Y A356193 Similar sequences: A053143, A053149, A053167, A066638, A087320, A087321, A197863, A356191, A356192, A356194.
%K A356193 nonn,easy,mult
%O A356193 1,2
%A A356193 _Amiram Eldar_, Jul 29 2022