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%I #44 Nov 19 2022 04:44:17
%S 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,
%T 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,
%U 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
%N 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.
%C 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
%H Reinhard Zumkeller, <a href="/A028234/b028234.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n / A028233(n).
%F A001221(a(n)) = A001221(n)-1; A001222(a(n)) = A001222(n)-A067029(n). - _Reinhard Zumkeller_, May 13 2006
%F 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
%t a[n_] := n / Power @@ First[FactorInteger[n]]; Table[a[n], {n, 1, 84}] (* _Jean-François Alcover_, Jun 12 2012 *)
%o (Haskell)
%o a028234 n = n `div` a028233 n -- _Reinhard Zumkeller_, Mar 27 2013
%o (PARI) a(n) = {my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f);} \\ _Michel Marcus_, Feb 11 2016
%o (Python)
%o from sympy import factorint
%o def a(n):
%o f = factorint(n)
%o return 1 if n==1 else n/(min(f)**f[min(f)]) # _Indranil Ghosh_, May 12 2017
%o (Scheme) (define (A028234 n) (/ n (A028233 n))) ;; Needs also code from A020639 and A028233. - _Antti Karttunen_, May 29 2017
%o (GAP) a := List(List(List(List([1..10^3], Factors), Collected), i -> i[1]), j -> j[1]^j[2]);;
%o A028234 := List([1..Length(a)],i->i/a[i]); # _Muniru A Asiru_, Jan 27 2018
%Y Cf. A001221, A001222, A002110, A005867, A020639, A028233, A067029.
%K nonn,nice,easy
%O 1,6
%A _Marc LeBrun_
%E Edited name to include a(1) = 1 by _Franklin T. Adams-Watters_, Jan 27 2018
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