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A328478 Divide n by the largest primorial that divides it and repeat until a fixed point is reached; a(n) is the fixed point.

%I A328478 #16 Jan 11 2022 03:21:48
%S A328478 1,1,3,1,5,1,7,1,9,5,11,1,13,7,15,1,17,3,19,5,21,11,23,1,25,13,27,7,
%T A328478 29,1,31,1,33,17,35,1,37,19,39,5,41,7,43,11,45,23,47,1,49,25,51,13,53,
%U A328478 9,55,7,57,29,59,1,61,31,63,1,65,11,67,17,69,35,71,1,73,37,75,19,77,13,79,5,81,41,83,7,85,43,87,11,89
%N A328478 Divide n by the largest primorial that divides it and repeat until a fixed point is reached; a(n) is the fixed point.
%H A328478 Antti Karttunen, <a href="/A328478/b328478.txt">Table of n, a(n) for n = 1..30030</a>
%H A328478 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A328478 If A111701(n) == n, then a(n) = n, otherwise a(n) = a(A111701(n)).
%F A328478 a(n) = n / A328479(n).
%t A328478 A111701[n_] := A111701[n] = Block[{m = n, k = 1}, While[IntegerQ[m/Prime[k]], m = m/Prime[k]; k++]; m];
%t A328478 a[n_] := a[n] = If[A111701[n] == n, n, a[A111701[n]]];
%t A328478 Array[a, 105] (* _Jean-François Alcover_, Jan 11 2022, after _Robert G. Wilson v_ in A111701 *)
%o A328478 (PARI)
%o A328478 A111701(n) = forprime(p=2, , if(n%p, return(n), n /= p));
%o A328478 A328478(n) = { my(u=A111701(n)); if(u==n, return(n), return(A328478(u))); };
%Y A328478 Cf. A007814 (gives the number of iterations to reach a fixed point), A025487 (indices of 1's).
%Y A328478 Cf. A002110, A053589, A111701, A328479.
%Y A328478 Cf. also A093411 for analogous sequence.
%K A328478 nonn
%O A328478 1,3
%A A328478 _Antti Karttunen_, Oct 19 2019
%E A328478 Definition clarified by _N. J. A. Sloane_, Jan 19 2021