A080398 Largest squarefree number dividing sum of divisors of n.

1, 3, 2, 7, 6, 6, 2, 15, 13, 6, 6, 14, 14, 6, 6, 31, 6, 39, 10, 42, 2, 6, 6, 30, 31, 42, 10, 14, 30, 6, 2, 21, 6, 6, 6, 91, 38, 30, 14, 30, 42, 6, 22, 42, 78, 6, 6, 62, 57, 93, 6, 14, 6, 30, 6, 30, 10, 30, 30, 42, 62, 6, 26, 127, 42, 6, 34, 42, 6, 6, 6, 195, 74, 114, 62, 70, 6, 42, 10

Offset

1,2

Comments

Not multiplicative, but satisfies a similar condition: For all coprime x, y (with gcd(x,y)=1), a(x*y) = LCM(a(x), a(y)), where LCM is the least common multiply of its arguments, A003990. Compare also with A351560. - Antti Karttunen, Feb 20 2022

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to lcm's

Index entries for sequences related to sigma(n)

Formula

a(n) = A007947(A000203(n)).

a(n) = A019565(A351560(n)). - Antti Karttunen, Feb 20 2022

Example

n=12:sigma[12]=1+2+3+4+6+12=28, sqf-kernel=14=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[1, w]], {w, 1, 100}]

Prog

(PARI) a(n) = factorback(factor(sigma(n))[, 1]); \\ Michel Marcus, Nov 18 2017

Crossrefs

Cf. A000203, A007947, A019565, A351560.

Sequence in context: A229120 A255067 A139285 * A126851 A082321 A057502

Adjacent sequences: A080395 A080396 A080397 * A080399 A080400 A080401

Keyword

nonn

Author

Labos Elemer, Mar 19 2003

Status

approved