%I #14 Jan 29 2020 02:57:00
%S 1,2,3,3,5,6,7,6,9,10,11,12,13,14,15,5,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,30,31,10,33,34,35,27,37,38,39,40,41,42,43,44,45,46,47,20,49,
%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,15,65,66,67,68,69,70,71,54,73,74,75,76,77,78,79,80,25,82,83,84,85,86,87,88,89,90,91,92,93,94,95,40
%N a(n) = min(n, A225546(n)).
%C For all i, j:
%C a(i) = a(j) => A331287(i) = A331287(j).
%H Antti Karttunen, <a href="/A331288/b331288.txt">Table of n, a(n) for n = 1..65537</a>
%t Array[If[# == 1, 1, Min[#, Times @@ Flatten@ Map[Function[{p, e}, Map[Prime[Log2@ # + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]]] &, 96] (* _Michael De Vlieger_, Jan 21 2020 *)
%o (PARI) A331288(n) = min(n, A225546(n));
%o (PARI)
%o A019565(n) = factorback(vecextract(primes(logint(n+!n, 2)+1), n));
%o A225546(n) = { my(f=factor(n)); for (i=1, #f~, my(p=f[i, 1]); f[i, 1] = A019565(f[i, 2]); f[i, 2] = 2^(primepi(p)-1); ); factorback(f); }; \\ From A225546
%o \\ If the following returns 1, then it is certainly true that A225546(p^e) > n (where p^e is one of the divisors of n), thus A225546(n) > n follows:
%o is_certainly_gt(p,e,n) = { my(b=A019565(e),j=(primepi(p)-1)); if(b>n,1,if((logint(b,2)*j)>logint(n,2),1,0)); };
%o A331288(n) = if((1==n)||isprime(n),n,my(f=factor(n)); for(i=1,#f~,if(is_certainly_gt(f[i,1],f[i,2],n),return(n))); min(n, A225546(n)));
%Y Cf. A225546, A225547, A331301, A331287.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 20 2020