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
Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Sum_{k>=0} A005867(k)/(prime(k+1)*(prime(k+1)+1)*A002110(k)) = 0.114813... . - Amiram Eldar, Nov 19 2022
MATHEMATICA
a[n_] := n / Power @@ First[FactorInteger[n]]; Table[a[n], {n, 1, 84}] (* Jean-François 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
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Edited name to include a(1) = 1 by Franklin T. Adams-Watters, Jan 27 2018
STATUS
approved