A073353 Sum of n and its squarefree kernel.

2, 4, 6, 6, 10, 12, 14, 10, 12, 20, 22, 18, 26, 28, 30, 18, 34, 24, 38, 30, 42, 44, 46, 30, 30, 52, 30, 42, 58, 60, 62, 34, 66, 68, 70, 42, 74, 76, 78, 50, 82, 84, 86, 66, 60, 92, 94, 54, 56, 60, 102, 78, 106, 60, 110, 70, 114, 116, 118, 90, 122, 124, 84, 66, 130, 132

Offset: 1

Author

Reinhard Zumkeller, Jul 29 2002

Keywords

• nonn
• easy

Comments

a(n) is even; a(n)=2*n iff n is squarefree.

Least k >n such that n divides k^n. - Benoit Cloitre, Oct 09 2002

a(n) is the smallest integer > n such that the positive integers coprime to a(n) are also coprime to n. - Leroy Quet, Dec 24 2006

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A005117, A065463, A066503, A064549, A003557, A073354, A078310.

Programs

Haskell

a073353 n = n + a007947 n  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

a[n_] := n + Times @@ FactorInteger[n][[;;, 1]]; Array[a, 100] (* Amiram Eldar, Dec 07 2023 *)

PARI

a(n)=vecprod(factor(n)[,1])+n \\ Charles R Greathouse IV, Nov 05 2017

Formula

a(n) = n + A007947(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 + A065463 = 1.704442... . - Amiram Eldar, Dec 07 2023