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A015050
Let m = A013929(n); then a(n) = smallest k such that m divides k^3.
5
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
OFFSET
1,1
LINKS
Henry Ibstedt, Surfing on the Ocean of Numbers, Erhus Univ. Press, Vail, 1997.
FORMULA
a(n) = A019555(A013929(n)).
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
MAPLE
isA013929 := proc(n)
not numtheory[issqrfree](n) ;
end proc:
A013929 := proc(n)
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:
A015050 := proc(n)
local m ;
m := A013929(n) ;
for k from 1 do
if modp(k^3, m) = 0 then
return k;
end if;
end do:
end proc:
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
R. Muller
EXTENSIONS
Description corrected by Diego Torres (torresvillarroel(AT)hotmail.com), Jun 23 2002
STATUS
approved