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

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

Author

R. Muller

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..10491
• Henry Ibstedt, Surfing on the Ocean of Numbers, Erhus Univ. Press, Vail, 1997.

Crossrefs

Cf. A013929, A015049, A015051, A019555.

Programs

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 *)

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

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

Extensions

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