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Let m = A013929(n); then a(n) = smallest k such that m divides k^4.
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%I #13 Jan 06 2024 09:21:03

%S 2,2,3,6,2,6,10,6,5,3,14,4,6,10,22,15,6,7,10,26,6,14,30,21,4,34,6,15,

%T 38,10,3,42,22,30,46,12,14,33,10,26,6,14,58,39,30,11,62,5,42,4,66,15,

%U 34,70,6,21,74,30,38,51,78,20,6,82,42,13,57,86

%N Let m = A013929(n); then a(n) = smallest k such that m divides k^4.

%H Amiram Eldar, <a href="/A015051/b015051.txt">Table of n, a(n) for n = 1..10000</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) = A053166(A013929(n)).

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * (zeta(2) * zeta(7) * Product_{p prime} (1-1/p^2+1/p^3-1/p^4+1/p^5-1/p^6) - 1)/(zeta(2)-1)^2 = 0.635465442379... . - _Amiram Eldar_, Jan 06 2024

%t f[p_, e_] := p^Ceiling[e/4]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* _Amiram Eldar_, Feb 10 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]/4)), ", ")));} \\ _Amiram Eldar_, Jan 06 2024

%Y Cf. A013929, A015050, A015049, A053166.

%K nonn

%O 1,1

%A R. Muller

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

%E Offset corrected by _Amiram Eldar_, Feb 10 2021