A080238 Largest squarefree number dividing sum of cubes of divisors of n.

1, 3, 14, 73, 42, 42, 86, 195, 757, 42, 222, 1022, 2198, 258, 42, 4681, 546, 2271, 70, 3066, 602, 222, 78, 2730, 15751, 6594, 5110, 6278, 8130, 42, 266, 4161, 1554, 546, 1806, 55261, 50654, 210, 2198, 2730, 22974, 1806, 39754, 16206, 31794, 78, 4326

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A007947(A001158(n)).

Example

n=12: sigma_3(12) = 1 + 8 + 27 + 64 + 216 + 1728 = 2044, sqf-kernel = 1022 = a(12).

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] cor[x_] := Apply[Times, ba[x]] Table[cor[DivisorSigma[3, w]], {w, 1, 100}]
Table[Max[Select[Divisors[Total[Divisors[n]^3]], SquareFreeQ]], {n, 50}] (* Harvey P. Dale, Sep 21 2022 *)

Crossrefs

Cf. A000213, A001157, A007947.

Sequence in context: A377113 A180187 A295104 * A307443 A213228 A306455

Adjacent sequences: A080235 A080236 A080237 * A080239 A080240 A080241

Keyword

nonn

Author

Labos Elemer, Mar 19 2003

Status

approved