%I #17 Jan 06 2024 09:20:57

%S 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 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 34,70,12,21,74,30,38,51,78,20,18,82,42,13,57,86

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

%H R. J. Mathar, <a href="/A015050/b015050.txt">Table of n, a(n) for n = 1..10491</a>

%H 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 a(n) = A019555(A013929(n)).

%F 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 isA013929 := proc(n)

%p not numtheory[issqrfree](n) ;

%p end proc:

%p A013929 := proc(n)

%p option remember;

%p local a;

%p if n = 1 then

%p 4;

%p else

%p for a from procname(n-1)+1 do

%p if isA013929(a) then

%p return a;

%p end if;

%p end do:

%p end if;

%p end proc:

%p A015050 := proc(n)

%p local m ;

%p m := A013929(n) ;

%p for k from 1 do

%p if modp(k^3,m) = 0 then

%p return k;

%p end if;

%p end do:

%p end proc:

%t 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 (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 Cf. A013929, A015049, A015051, A019555.

%K nonn

%O 1,1

%A R. Muller

%E Description corrected by Diego Torres (torresvillarroel(AT)hotmail.com), Jun 23 2002