%I #20 Jan 25 2020 02:33:01
%S 1,2,1,1,1,2,1,2,9,2,1,12,1,2,1,1,1,18,1,4,1,2,1,24,1,2,9,4,1,2,1,2,1,
%T 2,1,9,1,2,1,8,1,2,1,4,9,2,1,4,1,2,1,4,1,18,1,8,1,2,1,12,1,2,9,1,1,2,
%U 1,4,1,2,1,18,1,2,3,4,1,2,1,80,1,2,1,12,1,2,1,8,1,18,1,4,1,2,1,8,1,2,9,1,1,2,1,8,1
%N a(n) = gcd(n, A225546(n)).
%H Antti Karttunen, <a href="/A331287/b331287.txt">Table of n, a(n) for n = 1..11250</a>
%H Antti Karttunen, <a href="/A331287/a331287.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = gcd(n, A225546(n)).
%F a(n) = A331310(n) * A331311(n).
%F a(A297845(n,9)) = A297845(a(n),9). - _Peter Munn_, Jan 24 2020
%o (PARI) A331287(n) = gcd(n, A225546(n));
%o (PARI)
%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A331287(n) = if(1==n,1,my(f=factor(n),u=#binary(vecmax(f[, 2])),prods=vector(u,x,1),m=1,e); for(i=1,u,if(!(n%prime(i)),for(k=1,#f~, if(bitand(f[k,2],m),prods[i] *= f[k,1]))); m<<=1); prod(i=1,u,prime(i)^min(valuation(n,prime(i)),A048675(prods[i]))));
%Y Cf. A225546, A225547 (fixed points), A297845, A331288, A331310, A331311.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 20 2020