A015049 Let m = A013929(n); then a(n) = smallest k such that m divides k^2.

2, 4, 3, 6, 4, 6, 10, 12, 5, 9, 14, 8, 6, 20, 22, 15, 12, 7, 10, 26, 18, 28, 30, 21, 8, 34, 12, 15, 38, 20, 9, 42, 44, 30, 46, 24, 14, 33, 10, 52, 18, 28, 58, 39, 60, 11, 62, 25, 42, 16, 66, 45, 68, 70, 12, 21, 74, 30, 76, 51, 78, 40, 18, 82, 84, 13, 57, 86

Offset: 1

Author

R. Muller

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Henry Ibstedt, Surfing on the Ocean of Numbers, Erhus Univ. Press, Vail, 1997.

Crossrefs

Cf. A013929, A015050, A015051, A019554.

Programs

Mathematica

f[p_, e_] := p^Ceiling[e/2]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 10 2021 *)

PARI

lista(kmax) = {my(f); for(k = 2, kmax, f = factor(k); if(!issquarefree(f), print1(k/core(f, 1)[2], ", ")));} \\ Amiram Eldar, Jan 06 2024

Formula

a(n) = A019554(A013929(n)).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2)*(zeta(3)-1)/(zeta(2)-1)^2 = 0.799082... . - Amiram Eldar, Jan 06 2024

Extensions

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

Offset corrected by Amiram Eldar, Feb 10 2021