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A028234 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = n/p_1^e_1, with a(1) = 1. 140
1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 7, 5, 1, 1, 9, 1, 5, 7, 11, 1, 3, 1, 13, 1, 7, 1, 15, 1, 1, 11, 17, 7, 9, 1, 19, 13, 5, 1, 21, 1, 11, 5, 23, 1, 3, 1, 25, 17, 13, 1, 27, 11, 7, 19, 29, 1, 15, 1, 31, 7, 1, 13, 33, 1, 17, 23, 35, 1, 9, 1, 37, 25, 19, 11, 39, 1, 5, 1, 41, 1, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Together with A067029 is useful for defining sequences that are multiplicative with a(p^e) = f(e), as recurrences of the form: a(1) = 1 and for n > 1, a(n) = f(A067029(n)) * a(A028234(n)). - Antti Karttunen, May 29 2017

LINKS

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

FORMULA

a(n) = n / A028233(n).

A001221(a(n)) = A001221(n)-1; A001222(a(n)) = A001222(n)-A067029(n). - Reinhard Zumkeller, May 13 2006

MATHEMATICA

a[n_] := n / Power @@ First[FactorInteger[n]]; Table[a[n], {n, 1, 84}] (* Jean-Fran├žois Alcover, Jun 12 2012 *)

PROG

(Haskell)

a028234 n = n `div` a028233 n  -- Reinhard Zumkeller, Mar 27 2013

(PARI) a(n) = {my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); } \\ Michel Marcus, Feb 11 2016

(Python)

from sympy import factorint

def a(n):

    f = factorint(n)

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

(Scheme) (define (A028234 n) (/ n (A028233 n))) ;; Needs also code from A020639 and A028233. - Antti Karttunen, May 29 2017

(GAP) a := List(List(List(List([1..10^3], Factors), Collected), i -> i[1]), j -> j[1]^j[2]);;

A028234 := List([1..Length(a)], i->i/a[i]); # Muniru A Asiru, Jan 27 2018

CROSSREFS

Cf. A020639, A028233, A067029.

Sequence in context: A086767 A119288 A226040 * A052125 A214874 A081060

Adjacent sequences:  A028231 A028232 A028233 * A028235 A028236 A028237

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

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Last modified February 17 16:26 EST 2018. Contains 299296 sequences. (Running on oeis4.)