A152235 Largest squarefree number dividing the number of divisors n.

1, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 6, 2, 2, 2, 5, 2, 6, 2, 6, 2, 2, 2, 2, 3, 2, 2, 6, 2, 2, 2, 6, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 6, 6, 2, 2, 10, 3, 6, 2, 6, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 6, 7, 2, 2, 2, 6, 2, 2, 2, 6, 2, 2, 6, 6, 2, 2, 2, 10, 5, 2, 2, 6, 2, 2, 2, 2, 2, 6, 2, 6, 2, 2, 2, 6, 2, 6, 6, 3, 2, 2, 2, 2, 2

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = rad(tau(n)) = A007947(A000005(n)).

Mathematica

f[n_] := Last@ Select[ Divisors@ DivisorSigma[0, n], SquareFreeQ@# &]; Array[f, 105] (* Robert G. Wilson v, Dec 23 2008 *)

Prog

(Magma) [ 1 ] cat [ &*[ k[1]: k in Factorization(NumberOfDivisors(n)) ]: n in [2..105] ]; // Klaus Brockhaus, Dec 03 2008
(PARI) for(n=1, 50, print1(factorback(factorint(numdiv(n))[, 1]), ", ")) \\ G. C. Greubel, Jul 13 2017; corrected by Amiram Eldar, Sep 01 2019 *)

Crossrefs

Cf. A000005, A007947.

Sequence in context: A071188 A078545 A163105 * A278966 A374383 A123582

Adjacent sequences: A152232 A152233 A152234 * A152236 A152237 A152238

Keyword

easy,nonn

Author

Giovanni Teofilatto, Nov 30 2008

Extensions

Extended by Klaus Brockhaus, Dec 03 2008

Status

approved