A015051 Let m = A013929(n); then a(n) = smallest k such that m divides k^4.

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, 38, 10, 3, 42, 22, 30, 46, 12, 14, 33, 10, 26, 6, 14, 58, 39, 30, 11, 62, 5, 42, 4, 66, 15, 34, 70, 6, 21, 74, 30, 38, 51, 78, 20, 6, 82, 42, 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, A015049, A053166.

Programs

Mathematica

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 *)

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

Formula

a(n) = A053166(A013929(n)).

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

Extensions

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

Offset corrected by Amiram Eldar, Feb 10 2021