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A015050 Let m = A013929(n); then a(n) = smallest k such that m divides k^3.

%I A015050 #17 Jan 06 2024 09:20:57
%S A015050 2,2,3,6,4,6,10,6,5,3,14,4,6,10,22,15,12,7,10,26,6,14,30,21,4,34,6,15,
%T A015050 38,20,9,42,22,30,46,12,14,33,10,26,6,28,58,39,30,11,62,5,42,8,66,15,
%U A015050 34,70,12,21,74,30,38,51,78,20,18,82,42,13,57,86
%N A015050 Let m = A013929(n); then a(n) = smallest k such that m divides k^3.
%H A015050 R. J. Mathar, <a href="/A015050/b015050.txt">Table of n, a(n) for n = 1..10491</a>
%H A015050 Henry Ibstedt, <a href="http://www.gallup.unm.edu/~smarandache/Ibstedt-surfing.pdf">Surfing on the Ocean of Numbers</a>, Erhus Univ. Press, Vail, 1997.
%F A015050 a(n) = A019555(A013929(n)).
%F A015050 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * (zeta(2) * zeta(5) * Product_{p prime} (1-1/p^2+1/p^3-1/p^4) - 1)/(zeta(2)-1)^2 = 0.6611256641303... . - _Amiram Eldar_, Jan 06 2024
%p A015050 isA013929 := proc(n)
%p A015050     not numtheory[issqrfree](n) ;
%p A015050 end proc:
%p A015050 A013929 := proc(n)
%p A015050     option remember;
%p A015050     local a;
%p A015050     if n = 1 then
%p A015050         4;
%p A015050     else
%p A015050         for a from procname(n-1)+1 do
%p A015050             if isA013929(a) then
%p A015050                 return a;
%p A015050             end if;
%p A015050         end do:
%p A015050     end if;
%p A015050 end proc:
%p A015050 A015050 := proc(n)
%p A015050     local m ;
%p A015050     m := A013929(n) ;
%p A015050     for k from 1 do
%p A015050         if modp(k^3,m) = 0 then
%p A015050             return k;
%p A015050         end if;
%p A015050     end do:
%p A015050 end proc:
%t A015050 f[p_, e_] := p^Ceiling[e/3]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* _Amiram Eldar_, Feb 09 2021 *)
%o A015050 (PARI) lista(kmax) = {my(f); for(k = 2, kmax, f = factor(k); if(!issquarefree(f), print1(prod(i = 1, #f~, f[i,1]^ceil(f[i,2]/3)), ", ")));} \\ _Amiram Eldar_, Jan 06 2024
%Y A015050 Cf. A013929, A015049, A015051, A019555.
%K A015050 nonn
%O A015050 1,1
%A A015050 R. Muller
%E A015050 Description corrected by Diego Torres (torresvillarroel(AT)hotmail.com), Jun 23 2002