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A015050
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Let m = A013929(n); then a(n) = smallest k such that m divides k^3.
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5
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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, 38, 20, 9, 42, 22, 30, 46, 12, 14, 33, 10, 26, 6, 28, 58, 39, 30, 11, 62, 5, 42, 8, 66, 15, 34, 70, 12, 21, 74, 30, 38, 51, 78, 20, 18, 82, 42, 13, 57, 86
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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MAPLE
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isA013929 := proc(n)
not numtheory[issqrfree](n) ;
end proc:
option remember;
local a;
if n = 1 then
4;
else
for a from procname(n-1)+1 do
if isA013929(a) then
return a;
end if;
end do:
end if;
end proc:
local m ;
for k from 1 do
if modp(k^3, m) = 0 then
return k;
end if;
end do:
end proc:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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R. Muller
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EXTENSIONS
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Description corrected by Diego Torres (torresvillarroel(AT)hotmail.com), Jun 23 2002
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STATUS
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approved
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