login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071773 a(n) = gcd(rad(n), n/rad(n)), where rad(n) = A007947(n) is the squarefree kernel of n. 7
1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 5, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 7, 5, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 5, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 7, 3, 10, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

n is squarefree iff a(n)=1.

Product of primes dividing n more than once. - Charles R Greathouse IV, Aug 08 2013

Squarefree kernel of the square part of n. - Peter Munn, Jun 12 2020

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Squarefree.

FORMULA

a(n) = gcd(A007947(n), A003557(n)).

Multiplicative with p^e -> p^ceiling((e-1)/e), p prime.

a(n) = rad(n/rad(n)) = A007947(A003557(n)). - observed by Velin Yanev, Aug 20 2017, confirmed by Antti Karttunen, Nov 28 2017

a(n) = A007947(A057521(n)). - Antti Karttunen, Nov 28 2017

a(n) = A007947(A008833(n)). - Peter Munn, Jun 12 2020

MATHEMATICA

Table[With[{r = Apply[Times, FactorInteger[n][[All, 1]]]}, GCD[r, n/r]], {n, 104}] (* Michael De Vlieger, Aug 20 2017 *)

PROG

(PARI) a(n)=my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]>1)) \\ Charles R Greathouse IV, Aug 08 2013

(Scheme, with memoization-macro definec) (definec (A071773 n) (if (= 1 n) n (* (if (zero? (modulo n (expt (A020639 n) 2))) (A020639 n) 1) (A071773 (A028234 n))))) ;; Antti Karttunen, Nov 28 2017

CROSSREFS

Cf. A003557, A005117, A007947, A007948, A008833, A057521.

Sequence in context: A205792 A249739 A249740 * A308993 A000188 A162401

Adjacent sequences:  A071770 A071771 A071772 * A071774 A071775 A071776

KEYWORD

nonn,mult

AUTHOR

Reinhard Zumkeller, Jun 24 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 8 13:59 EST 2021. Contains 341949 sequences. (Running on oeis4.)