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A365427 a(n) = A336467(A163511(n)).

%I A365427 #9 Sep 03 2023 18:21:09
%S A365427 1,1,1,1,1,1,1,3,1,1,1,9,1,3,3,1,1,1,1,27,1,9,9,1,1,3,3,3,3,1,1,3,1,1,
%T A365427 1,81,1,27,27,1,1,9,9,3,9,1,1,9,1,3,3,9,3,3,3,3,3,1,1,9,1,3,3,7,1,1,1,
%U A365427 243,1,81,81,1,1,27,27,3,27,1,1,27,1,9,9,9,9,3,3,9,9,1,1,27,1,9,9,49,1,3,3,27,3
%N A365427 a(n) = A336467(A163511(n)).
%H A365427 Antti Karttunen, <a href="/A365427/b365427.txt">Table of n, a(n) for n = 0..16385</a>
%F A365427 For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%o A365427 (PARI)
%o A365427 A000265(n) = (n>>valuation(n,2));
%o A365427 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A365427 A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
%o A365427 A365427(n) = A336467(A163511(n));
%Y A365427 Cf. A000265, A163511, A336467.
%Y A365427 Cf. also A365426.
%K A365427 nonn
%O A365427 0,8
%A A365427 _Antti Karttunen_, Sep 03 2023