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

1,1

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

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

Mathematica

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

Prog

(Haskell)
a073353 n = n + a007947 n  -- Reinhard Zumkeller, Jul 23 2013
(PARI) a(n)=vecprod(factor(n)[, 1])+n \\ Charles R Greathouse IV, Nov 05 2017

Crossrefs

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

Sequence in context: A053568 A037225 A060685 * A254734 A254733 A254732

Adjacent sequences: A073350 A073351 A073352 * A073354 A073355 A073356

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jul 29 2002

Status

approved