A102631 - OEIS

A102631

a(n) = n^2 / (squarefree kernel of n).

1, 2, 3, 8, 5, 6, 7, 32, 27, 10, 11, 24, 13, 14, 15, 128, 17, 54, 19, 40, 21, 22, 23, 96, 125, 26, 243, 56, 29, 30, 31, 512, 33, 34, 35, 216, 37, 38, 39, 160, 41, 42, 43, 88, 135, 46, 47, 384, 343, 250, 51, 104, 53, 486, 55, 224, 57, 58, 59, 120, 61, 62, 189, 2048, 65, 66, 67

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Index of first occurrence of n in A019554. - Franklin T. Adams-Watters, Nov 17 2006

LINKS

Michel Marcus, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = A000290(n)/A007947(n) = n*A003557(n);

a(n) = n iff n is squarefree: a(A005117(n)) = A005117(n).

Multiplicative with a(p^e) = p^{2e-1}. - Franklin T. Adams-Watters, Nov 17 2006

Dirichlet g.f.: Product_{p prime} (1 - p/(p^2 - p^s)). - Amiram Eldar, Aug 28 2023

a(n) = A350390(n^2). - Amiram Eldar, Nov 30 2023

MATHEMATICA

a[n_] := n^2/Times @@ FactorInteger[n][[All, 1]];

Array[a, 70] (* Jean-François Alcover, Jun 11 2019 *)

PROG

(Sage)

def A102631(n) :

p = n

for a in factor(n) :

if a[1] > 1 :

p = p * a[0]^(a[1]-1)

return p

[A102631(n) for n in (1..67)] # Peter Luschny, Feb 07 2012

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 2] = 2*f[k, 2]-1); factorback(f); \\ Michel Marcus, Aug 20 2017

CROSSREFS

Cf. A000290, A007947, A003557, A005117, A019554, A350390.

Sequence in context: A157488 A188385 A332793 * A100782 A110340 A183091

Adjacent sequences: A102628 A102629 A102630 * A102632 A102633 A102634

KEYWORD

nonn,easy,mult

AUTHOR

Reinhard Zumkeller, Feb 25 2005

STATUS

approved