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

Author

Labos Elemer, Mar 19 2003

Keywords

• nonn

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

Examples

			n=12:sigma[12]=1+2+3+4+6+12=28, sqf-kernel=14=a(12)
		

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)

Crossrefs

Cf. A000203, A007947, A019565, A351560.

Programs

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}]

PARI

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

Formula

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

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