login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A028233 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = p_1^e_1, with a(1) = 1. 24
1, 2, 3, 4, 5, 2, 7, 8, 9, 2, 11, 4, 13, 2, 3, 16, 17, 2, 19, 4, 3, 2, 23, 8, 25, 2, 27, 4, 29, 2, 31, 32, 3, 2, 5, 4, 37, 2, 3, 8, 41, 2, 43, 4, 9, 2, 47, 16, 49, 2, 3, 4, 53, 2, 5, 8, 3, 2, 59, 4, 61, 2, 9, 64, 5, 2, 67, 4, 3, 2, 71, 8, 73, 2, 3, 4, 7, 2, 79, 16, 81, 2, 83, 4, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Highest power of smallest prime dividing n. - Reinhard Zumkeller, Apr 09 2015

LINKS

T. D. Noe and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000, first 1000 terms from T. D. Noe

FORMULA

a(n) = A020639(n)^A067029(n). - Reinhard Zumkeller, May 13 2006

a(n) = A141809(n,1). - Reinhard Zumkeller, Jun 04 2012

a(n) = n / A028234(n). - Antti Karttunen, May 29 2017

EXAMPLE

From Muniru A Asiru, Jan 27 2018: (Start)

If n=10, then a(10) = 2 since 10 = 2^1*5^1.

If n=16, then a(16) = 16 since 16 = 2^4.

If n=29, then a(29) = 29 since 29 = 29^1.

(End)

MAPLE

A028233 := proc(n)

    local spf, pf;

    if n = 1 then

        return 1 ;

    end if;

    spf := A020639(n) ;

    for pf in ifactors(n)[2] do

        if pf[1] = spf then

            return pf[1]^pf[2] ;

        end if;

    end do:

end proc: # R. J. Mathar, Jul 09 2016

# second Maple program:

a:= n-> `if`(n=1, 1, (i->i[1]^i[2])(sort(ifactors(n)[2])[1])):

seq(a(n), n=1..100);  # Alois P. Heinz, Jan 29 2018

MATHEMATICA

a[n_] := Power @@ First[ FactorInteger[n]]; Table[a[n], {n, 1, 86}] (* Jean-Fran├žois Alcover, Dec 01 2011 *)

PROG

(Haskell)

a028233 = head . a141809_row

-- Reinhard Zumkeller, Jun 04 2012, Aug 17 2011

(PARI) a(n)=if(n>1, n=factor(n); n[1, 1]^n[1, 2], 1) \\ Charles R Greathouse IV, Apr 26 2012

(Python)

from sympy import factorint

def a(n):

    f = factorint(n)

    return 1 if n==1 else min(f)**f[min(f)] # Indranil Ghosh, May 12 2017

(Scheme)

;; Naive implementation of A020639 is given under that entry. All of these functions could be also defined with definec to make them faster on the later calls. See http://oeis.org/wiki/Memoization#Scheme

(define (A028233 n) (if (< n 2) n (let ((lpf (A020639 n))) (let loop ((m lpf) (n (/ n lpf))) (cond ((not (zero? (modulo n lpf))) m) (else (loop (* m lpf) (/ n lpf)))))))) ;; Antti Karttunen, May 29 2017

(GAP) List(List(List(List([1..10^3], Factors), Collected), i -> i[1]), j -> j[1]^j[2]); # Muniru A Asiru, Jan 27 2018

CROSSREFS

Cf. A020639, A006530, A034684, A034699, A053585.

See also A028234.

Cf. A008475.

Cf. A141809.

Sequence in context: A081811 A304181 A034684 * A216972 A066296 A162961

Adjacent sequences:  A028230 A028231 A028232 * A028234 A028235 A028236

KEYWORD

nonn,nice,easy

AUTHOR

Marc LeBrun

EXTENSIONS

Edited name to include a(1) = 1 by Franklin T. Adams-Watters, Jan 27 2018

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)